use strict;

my %B_rids;

# ... open file B, read it to fill %B_rids hash, then: 

my @A_files = ... # do something to get list of A file paths/names

for my $A_file ( @A_files ) {
    unless ( open( my $afh, "<", $A_file )) {
              # update: you'll add encoding on 2nd arg, e.g. "<:utf8"
        warn "Open failed for $A_file: $!\n";
        next;
    } 
    while (<$afh>) {
        chomp;
        my @fields = split /\t/;
        if ( exists( $B_rids{ $fields[4] } )) { # does rid1 exist in B?
            # do something
        }
        elsif ( exists( $B_rids{ $fields[5] } )) { # does rid2 exist in B?
            # do something else
        }
    }
}