I'm trying to find a regex that will...

You don't need no steenkin' regex:

open my $fh, '<', 'whatever'; # or whatever

my %hash = ( a => 0, e => 1, i => 2, o => 3, u => 4 );

while ( <$fh> ) {
  chomp;
  
  my $copy = $_;
  my @array;

  while ( my $char = lc chop $copy ) {
    no warnings 'uninitialized';
    $array[ $hash{ $char } ] = 1;
  }

  say if ( grep $_, @array ) == 5;
}
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Pretty fast, too, you'll find...

Update: Hmm, if you take out the line no warnings 'uninitialized'; (and therefore remove use warnings or whatever from the start of the code), it seems to run nearly 20% faster still...

Comments welcome.

Update 2: Oops, just realised that my code doesn't work! Change the contents of the inner while loop to:

$array[ $hash{ $char } ] = 1 if defined $hash{ $char };

Which is what I had originally, before playing with no warnings 'uninitialized';. And then I didn't test properly.

Mea culpa.