Firstly, $a and $b are best avoided as variable names as they are pre-declared for use with the sort function. You could do this task by splitting one string on spaces (assuming your data is always space delimited) to populate a hash and then splitiing the second string and checking if any part of that exists already in the hash.

use strict;
use warnings;

my $str1 = q{PF01389    6    218    1    255    430.09};
my $str2 = q{PF00691    PF01389};

my %str1Hash = map {$_ => 1} split m{\s+}, $str1;

foreach my $possible (split m{\s+}, $str2)
{
    print qq{$possible common\n}
       if exists $str1Hash{$possible};
}
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I hope this is of use.

Cheers,

JohnGG