Not only is the above badly formatted, it occured to me to test additional possibilities; so (with apologies), revised, cleaned up, etc. :

#!C:/perl/bin -w

my @testitems = qw( aaa_gjh1_dfgdf_0009 
                    aaa_gjh_0000 
                    aaa_gjh1_DFgdf_0009
                    aaa_fdsfs_000
                    aaa_sdf_jdsh_01111 
                    aaa_gjh1_dfgdf_0009 
                    aaa_gjhi0000
                    aaa_gjh1_df<:df_0009 
                    aaa_gjh_0000 
                    aaa_ABCDEFGHI123456789ZYXW_1111
                    aaa_ABCDEFGHI123456789ZYXWVUT_1111);
                           # next to last: 23 before the last underlin
+e  
                           # last element: more than 24 intermediate c
+hars

for my $item(@testitems) {
  if ( $item =~ m/
     ^aaa_              # starts with "aaa_"
     [_A-Za-z0-9]{1,23} # test next 1,23 chars: underline, alphas or d
+ecimal_nums
     (?<=\D)            # Pos_LookBehind, Last char BEFORE last 4 (may
+ be the 24th) 
                              # can't be a digit else we may find 5 di
+gits at the end
     \d{4}$             # has ONLY - emphasis mine - four digits at th
+e end
    /x ) {
            print "MATCHES:  $item\n";
    } else {
    print "NO match: $item\n";
    }
}

print "done\n";

=head1 OUTPUT:
MATCHES:  aaa_gjh1_dfgdf_0009
MATCHES:  aaa_gjh_0000
MATCHES:  aaa_gjh1_DFgdf_0009                   # caps are alpha; OP m
+ay want only lc
NO match: aaa_fdsfs_000                         # only 3 digits at end
+ of string
                                                     # (contrary to sp
+ec)
NO match: aaa_sdf_jdsh_01111                    # 5 digits at end of s
+tring
                                                     # (contrary to sp
+ec)
MATCHES:  aaa_gjh1_dfgdf_0009
MATCHES:  aaa_gjhi0000                          # no underscore before
+ final 4 digits
                                                     # (ok per spec)
NO match: aaa_gjh1_df<:df_0009                  # includes symbol and 
+punct 
                                                     # (contrary to sp
+ec)
MATCHES:  aaa_gjh_0000
MATCHES:  aaa_ABCDEFGHI123456789ZYXW_1111       # < 24 chars before fi
+nal 4 digits 
                                                      # (ok per spec)
NO match: aaa_ABCDEFGHI123456789ZYXWVUT_1111    # > 24 chars before fi
+nal 4 digits 
                                                      # (contrary to s
+pec)
done
=cut
[download]

But see grinder's elegant (and earlier) node, below!