Pure Bash - no external utilities, 66

Thanks to @Nahuel Fouilleul for saving 10 bytes!

printf "`echo %3s{,,}{,,,}`\n" '' {0..10} $[{1..5}*{1,{0..50..5}}]

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Ruby, 77 bytes

Improvements thanks to Dingus

q=*r=1..10;s=" "
1.upto(6){|i|puts"  #{s} "+("%4d"*10)%q
q=r.map{|j|j*5*s=i}}

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Ruby, 82 bytes

q=r=[*1..10];s=" "
1.upto(6){|i|puts ("  #{s} "+"%4d"*10)%q
s=i;q=r.map{|j|j*i*5}}

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SQL, Will never win 267

with C AS(SELECT 10 C UNION ALL SELECT C-1FROM C WHERE C-1>=0),M AS(SELECT 5 M UNION ALL SELECT M-1FROM M WHERE M-1>0),PS as(select C,M,C*M*5 PS from C cross join M)SELECT*FROM(SELECT*FROM PS)tbl PIVOT(max(PS)FOR C IN ([0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]))P

Try it here db<>fiddle

Explained...

--List Crystals 0-10
with Crystal AS (
    SELECT 10 Crystal
UNION ALL
    SELECT Crystal-1
    FROM Crystal
    WHERE Crystal-1>=0
    )
--List Members 1-5
,Member AS (
    SELECT 5 Member
UNION ALL
    SELECT Member-1
    FROM Member
    WHERE Member-1>0
    )
--Join Crystal and Member, Calc People Seconds
,PS as
(
    select Crystal,Member,Crystal*Member*5 PS
    from Crystal
    cross join Member
)
--Pivot Maze
SELECT * FROM   
    (
    SELECT *
    FROM PS
    ) tbl 
PIVOT(
    max(PS)
    FOR Crystal IN ([0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10])
    ) pvt

Java, 112 bytes

v->{var r="";for(int i=-1,j;i++<5;r+="\n")for(j=-2;j++<10;)r+=r.format("%4s",i<1?j<0?r:j:j<0?i:i*j*5);return r;}

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Explanation:

v->{                      // Method with empty unused parameter and String return-type
  var r="";               //  Result-String, starting empty
  for(int i=-1,j;i++<5    //  Loop `i` in the range (-1,5]:
      ;                   //    After every iteration:
       r+="\n")           //     Append a newline to the result-String
    for(j=-2;j++<10;)     //   Inner loop `j` in the range (-2,10]:
      r+=r.format("%4s",  //    Append the following with up to 4 leading spaces to the
                          //    result-String:
          i<1?i<j?        //     If it's the first row and column:
            r             //      Append the result-String itself, which is still "" at
                          //      this point
          :               //     Else-if it's the first row, but NOT the first column:
            j             //      Append `j`
          :j<0?           //     Else-if it's the first column, but NOT the first row:
            i             //      Append `i`
          :               //     Else (it's neither the first row nor column):
            i*j*5);       //      Append `i` multiplied by `j` multiplied by 5
  return r;}              //  After the nested loops, return the result-String

Vyxal, 115 bits^v1, 14.375 bytes

5ƛ₀ʀ*5*J;₀ʀðppÞĠ

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Explained

5ƛ₀ʀ*5*J;₀ʀðppÞĠ­⁡​‎‎⁡⁠⁡‏⁠‎⁡⁠⁢‏⁠‎⁡⁠⁣⁡‏‏​⁡⁠⁡‌⁢​‎‎⁡⁠⁣‏⁠‎⁡⁠⁤‏⁠‎⁡⁠⁢⁡‏‏​⁡⁠⁡‌⁣​‎‎⁡⁠⁢⁢‏⁠‎⁡⁠⁢⁣‏‏​⁡⁠⁡‌⁤​‎‎⁡⁠⁢⁤‏‏​⁡⁠⁡‌⁢⁡​‎‎⁡⁠⁣⁢‏⁠‎⁡⁠⁣⁣‏⁠‎⁡⁠⁣⁤‏⁠‎⁡⁠⁤⁡‏‏​⁡⁠⁡‌⁢⁢​‎‎⁡⁠⁤⁢‏‏​⁡⁠⁡‌⁢⁣​‎‎⁡⁠⁤⁣‏⁠‎⁡⁠⁤⁤‏‏​⁡⁠⁡‌­
5ƛ      ;         # ‎⁡To each number in the range [1, 5]:
  ₀ʀ*             # ‎⁢  Multiply it by the range [0, 10]
     5*           # ‎⁣  Multiply that by 5
       J          # ‎⁤  And prepend the number to the start of the list
         ₀ʀðp     # ‎⁢⁡The list [0, 10] with " " prepended
             p    # ‎⁢⁢Put that list at the start of the list of lists from before
              ÞĠ  # ‎⁢⁣Gridify, right-aligning and joining columns on spaces.
💎

Created with the help of Luminespire.

Jelly, 16 bytes

⁵Żð⁶;W;Gµ5×1;×þ5

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   ð⁶;W;Gµ          [[" "] + a] + f(a), as a grid
                    where
 ⁵Ż                 a    = [0…10]
          5×1;×þ5   f(r) = table of [1]+(5×r) times [1…5]

05AB1E, 22 bytes

5LTÝδ*5*TÝšεNš}§3j»ð2ǝ

Should have been 21 bytes without the §, but unfortunately there is a bug in 05AB1E.

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Explanation:

5LTÝδ*           # Push a 0..10 by 1..5 multiplication table:
5L               #  Push a list in the range [1,5]
  TÝ             #  Push a list in the range [0,10]
    δ            #  Pop both lists, and apply double-vectorized:
     *           #   Multiply the values together
      5*         # Multiply each value by 5
        TÝš      # Prepend list [0,10] to this matrix
           ε  }  # Map over each row:
            Nš   #  Prepend the 0-based map-index to the list
§                # (workaround: cast every integer to a string)
 3j              # Prepend leading spaces where necessary so each string is of length 3
   »             # Join each inner list of strings with space delimiter,
                 # and then each string with newline delimiter
      ǝ          # Replace the character 
     2           # at (0-based) index 2 (which is the first '0')
    ð            # with a space
                 # (after which the result is output implicitly)

BQN (CBQN), 128 bytes

This is definitely sub-optimal. I don't really know what I'm doing with this language.

•Out ¯1↓⥊(1↓˘∾˘⍉(/⟜" "∘(4-≠)∾⊢)¨•Fmt¨[↕6]∾⍉[↕11]∾5××´¨1↓↕6‿11)∾˘6‿1⥊@+10

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Kotlin, 118 bytes 97 bytes

fun main() = println((0..5).joinToString("\n") { j -> (0..10).joinToString(" ") { i -> "${i * j * 5}".padStart(3) } })

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I've removed about 21 bytes thanks to The Thonnu because I forgot to remove spaces, also I've used "%3d".format() to pad the numbers to a width of 3 characters.

fun main()=println((0..5).joinToString("\n"){j->(0..10).joinToString(" "){"%3d".format(it*j*5)}})

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Python 3, 76 bytes

print(*(' '.join(f'{i*j*5:3}'for i in range(11))for j in range(6)),sep='\n')

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C (clang), 99 bytes

p(r,i){r?printf("\n%d",r):0;for(i=-1;i++<10;printf("\t%d",r>0?i*5*r:i));}f(i){for(i=0;i<6;p(i++));}

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Excel (ms365), 145, 122 bytes

• -23 bytes thanks to @JosWoolley

Formula in A1:

=LET(x,ROW(1:6)-1,y,COLUMN(A:K)-1,TEXTJOIN(HSTACK(IF(y+1," "),CHAR(10)),,RIGHT("  "&HSTACK(IF(x,x," "),IF(x,y*5*x,y)),3)))

This can be 117 bytes if we would swap CHAR(10) out for a literal Alt+Enter:

=LET(x,ROW(1:6)-1,y,COLUMN(A:K)-1,TEXTJOIN(HSTACK(IF(y+1," "),"
"),,RIGHT("  "&HSTACK(IF(x,x," "),IF(x,y*5*x,y)),3)))

Python 3, 69 bytes

for k in b"
\n":print(('%4s'*12%(k//5or'',*range(0,11*k,k)))[1:])

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Thanks to dingledooper for -3 bytes from the bytestring hardcode. If trailing spaces are allowed:

64 bytes

for k in b"
\n":print('%3s '*12%(k//5or'',*range(0,11*k,k)))

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Python, 97 bytes

[print(("%4s"*12%x)[1:])for x in[(" ",*range(11))]+[(c,*range(0,c*50+1,5*c))for c in range(1,6)]]

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Perl 5, 76 bytes

printf$"x3 .($b="%4d"x11),0..10;//,printf"
  $_$b",map$_*=5*$',0..10for 1..5

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Jelly, 19 bytes

-r⁵×þ`ḣ7ẸƇ»×¥5AG⁶3¦

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How?

-r⁵×þ`ḣ7ẸƇ»×¥5AG⁶3¦ - Main Link: no arguments
-r⁵                 - -1 inclusive range 10 -> [-1,0,1,2,3,4,5,6,7,8,9,10]
     `              - use as both arguments of:
    þ               -   table with:
   ×                -     multiplication
      ḣ7            - head to index seven
         Ƈ          - keep those for which:
        Ẹ           -   any?
            ¥5      - last two links as a dyad - f(M=that, 5):
           ×        -   {M} multiply {5}
          »         -   {M} maximum {that}
                      (multiplies M's positive values by 5)
              A     - absolute values
               G    - format as a grid
                  ¦ - sparse application...
                 3  - ...to indices: [3]
                ⁶   - ...action: a space character
                      (replaces the top left 5 (from -1×-1×5) with a space)

R, 60 bytes

write(format(rbind(c("",1:5),0:10%o%c(1,1:5*5)),j="r"),1,12)

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Retina, 67 bytes

   11*#5*$(¶_11*@
_
$>:&
#
 $:&
%`@(?<=(.).*)
 $.($1*$:&*5*
P^`\d+

Try it online! Explanation:

   11*#5*$(¶_11*@

Insert a template for the output: 11 column headers, and 5 rows, each with a header.

_
$>:&

Populate the row headers. $>:& translates as 1-indexed match index.

#
 $:&

Populate the column headers. $:& is the 0-indexed match index.

%`@(?<=(.).*)
 $.($1*$:&*5*

Populate the table body. Each row is processed independently, and each @'s match index is multiplied by the row number and by 5.

P^`\d+

Left-pad all of the numbers to the same width.

Bash, 138 bytes

(echo;seq 0 10;paste -d' ' <(seq 5) <(printf %s\\n {1..5}\*{0..10}\*5|bc|xargs -n11)|tr \  \\n)|sed 's/^/printf %3s\\\\n /e'|pr -ats\  -12

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With comments

This solution works by generating all the desired numbers, one per line, and then formatting the table with printf(1) and pr(1):

(
  # Generate the top line
  echo
  seq 0 10            

  # Intersperse 1 through 5 in-between the calculated rows using paste(1).
  # The calculation is done with a cross-product of {1..5}*{0..10}*5 piped
  # to bc(1).
  paste -d' ' \
    <(seq 5)  \
    <(\
        printf '%s\n' {1..5}\*{0..10}\*5 |
        bc                               |
        xargs -n11                       \
     ) |
  tr ' ' '\n' \
) |

# All columns should be 3 characters wide.
sed 's/^/printf "%3s\\n" /e' |

# Use pr(1) to output data across (-a), no header (-t) and with a space
# separator (-s ' ') between the 12 columns (-12).
pr -ats' ' -12

Charcoal, 26 25 bytes

Ｅ⁶⪫Ｅ¹²◧⎇λＩ×⊖λ∨×⁵ι¹⎇ιＩιω³ 

Try it online! Link is to verbose version of code. Explanation:

 ⁶                          Literal integer `6`
Ｅ                           Map over implicit range
    ¹²                      Literal integer `12`
   Ｅ                        Map over implicit range
       ⎇λ                   If not the first column
            λ               Current column
           ⊖                Decremented
          ×                 Multiplied by
                ι           Current row
              ×             Multiplied by
               ⁵            Literal integer `5`
             ∨              Logical Or
                 ¹          Literal integer `1`
         Ｉ                  Cast to string
                  ⎇ι        If not the first row
                    Ｉι      Current row as a string
                      ω     Else empty string
      ◧                ³    Left-pad to length 3
  ⪫                         Join with spaces
                            Implicitly print

23 22 bytes using the newer version of Charcoal on ATO:

Ｅ⁶⪫Ｅ¹²◧⎇λ×⊖λ∨×⁵ι¹∨ιω³ 

Attempt This Online! Link is to verbose version of code. Explanation: PadLeft stringifies its argument, allowing the removal of two instances of Cast and the subsequent simplification of Ternary to Or.

JavaScript (ES6), 74 bytes

+4 bytes for a quick and dirty fix to comply with the updated output

f=(y=5,x=11)=>x--?f(y,x)+`   ${x*y*5||x}`.slice(-4):y?f(y-1)+`
  `+y:'   '

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Commented

f = (                    // f is a recursive function taking:
  y = 5,                 //   y = team members
  x = 11                 //   x = crystals
) =>                     //
x-- ?                    // if x is not 0 (decrement it afterwards):
  f(y, x) +              //   do a recursive call with (x, y)
  `   ${x * y * 5 || x}` //   and append x * y * 5 or x if this is 0
  .slice(-4)             //   right-justified to 4 characters
                         //   with leading spaces
:                        // else:
  y ?                    //   if y is not 0:
    f(y - 1) +           //     do a recursive call with just y-1 (which
                         //     means that x is implicitly reset to 11)
    `\n  ` +             //     followed by a line feed a 2 spaces
    y                    //     followed by y
  :                      //   else:
    '   '                //     insert the 3 top-left spaces and stop

Thunno 2 N, 21 bytes

5ıTĖ×5×nƤð4ṙ;TĖðƤð4ṙƤ

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Explanation

5ı           # Map over [1..5]:
  TĖ×        #  Multiply by [0..10]
     5×      #  And multiply by 5
       nƤ    #  Prepend the current number
         ð4ṙ #  Right-justify to length 4
;            # End map
 TĖ          # Push [0..10]
   ðƤ        # Prepend a space
     ð4ṙ     # Right-justify to length 4
        Ƥ    # Prepend this list
             # Implicit output, joined on newlines