Change the 5th occurrence of whoever/whomever in $_ to whosoever/whomsoever. Here's a little more detail in a slight rewrite:

my $count=0;
$_ =~ s/ ((whom?)ever)          # whom? is in $2, whom?ever is in $1
       / if ( ++$count == 5 )   # for the fifth match
         {
             "${2}soever";      # set to whom?soever
         }
         else
         {
             $1;                # leave it as it is
         }
       /igex; # case (i)nsensitive, (g)lobal match, (e)xecute replace 
+string.
           # (x) ignore whitespace (added for this code example)
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ps - I hope your tutor reads Perlmonks :)