You start with @array1 but I think is better to cycle @array2 which seems governing your output.

use strict;
use warnings;

my @array1 = (1..5);
my @array2 = ('a','b','c','d','e','f','g');
my @array3 = ('I', 'II', 'III');

foreach my $letter(@array2){
    foreach my $index_roman(0..$#array3){
        foreach my $index (0..$#array1){
        print "$array1[$index],$letter,$array3[$index_roman]\n";
        }
    }
}
[download]

PS as wisely said by hippo, cycling indexes is no more needed, so semplified nested loop will be:

foreach my $letter(@array2){
    foreach my $roman(@array3){
        foreach my $number (@array1){
        print "$number,$letter,$roman\n";
        }
    }
}
[download]

L*