my $query = $db->prepare("select code, username, userid from transacti
+ons");
  $query->execute();
  my %code = map { $_ => [] } 0 .. 13;
  while (my $r = $qeury->fetchrow_hashref()) {
    my $c = $$r{code};
    push @{$code{$c}}, $r;
  }
  # For each code $c, $code{$c} is now an arrayref which
  # contains the relevant records (as hashrefs).  The
  # number of elements in the array equals the number
  # of occurances.  Now, for the second part...
  my %topfive;
  for my $c (keys %code) {
      my %user;
      for my $row (@{$code{$c}}) {
         # Note: this assumes that the userid field
         # is unique to each user.
         $user{$$row{userid}}{count}++;
         $user{$$row{userid}}{name} = $$row{username};
      }
      $topfive{$c} = [(sort {
        $$b[2] <=> $$a[2]
      } map {
        [$_, $user{$_}{name}, $user{$_}{count}]
      } keys %user)[0 .. 4]];     
  }
[download]

Maybe you should ask the monk who wrote it directly then? That's why we have threaded replies here. Anyway:

This prepares and executes an SQL statement, see DBI:

my $query = $db->prepare("select code, username, userid from transacti
+ons");
  $query->execute();
[download]

This initializes the %code hash with the keys from 0 to 13. See perlop about the range operator, map and then Data::Dumper for how to inspect data structures.

  my %code = map { $_ => [] } 0 .. 13;
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This line contains a typo that use strict; will catch for you. See strict and likely then Coping with Scoping.

  while (my $r = $qeury->fetchrow_hashref()) {
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This loop overall fetches each retrieved hash and puts it into the corresponding array in %code:

    my $c = $$r{code};
    push @{$code{$c}}, $r;
  }
  # For each code $c, $code{$c} is now an arrayref which
  # contains the relevant records (as hashrefs).  The
  # number of elements in the array equals the number
  # of occurances.  Now, for the second part...
[download]

This code determines the top five userids.

  my %topfive;
  for my $c (keys %code) {
      my %user;
      for my $row (@{$code{$c}}) {
         # Note: this assumes that the userid field
         # is unique to each user.
         $user{$$row{userid}}{count}++;
         $user{$$row{userid}}{name} = $$row{username};
      }
      $topfive{$c} = [(sort {
        $$b[2] <=> $$a[2]
      } map {
        [$_, $user{$_}{name}, $user{$_}{count}]
      } keys %user)[0 .. 4]];     
  }
[download]

I already recommended pushing more work back into the database instead of manually sorting and counting.