You could use Set::IntSpan:

use Set::IntSpan;

my $r1 = Set::IntSpan->new([ 5 .. 15 ]);
my $r2 = Set::IntSpan->new([ 2 .. 20 ]);

my $i = $r1->intersect($r2);

if ( !$i->empty and ( $i->max - $i->min ) >= 5 ) # criteria
{
    print "hit\n";
}
else
{
    print "miss\n";
}
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