It seems to me that no searching is required, as all the relevant information already present in the input data.

A grossly over elaborate coding is:

#! perl -slw
use strict;

my $s1 = "1,0,CTGCCACCGCTGT";
my $s2 = "1,5,ACCGCTGTGTTTCGGCCGGCGA";

my @s1 = split ',', $s1;
my @s2 = split ',', $s2;

if( $s1[0] == $s2[0] ) {
    if( $s1[1] > $s2[1] ) {
        my @temp = @s1;
        @s1 = @s2;
        @s2 = @temp;
    }
    if( $s2[1] < length( $s1 ) ) {
        ## Updated to correct the error pointed out by Lima1++ below
        my $l1 = length( $s1[2] ) - $s1[1] - $s2[1];
        my $l2 = length( $s2[2] );
        $l1 = $l2 if $l2 < $l1;
        
        print "The intersection between the strings:\n",
            $s1[2], "\n",
            ' ' x ( $s2[1] - $s1[1] ), $s2[2],
            "\nis\n", ' ' x $s2[1],
            substr $s1[2], $s2[1] - $s1[1], $l1;              ;

        print "\nand it occurs at a 1-based offset into the sequence o
+f ",
            $s2[1] + 1;
    }
    else {
        print "The strings do not intersect";
    }
}
else {
    print 'Strings are not from the same sequence';
}

__END__
c:\test>junk
The intersection between the strings:
CTGCCACCGCTGT
     ACCGCTGTGTTTCGGCCGGCGA
is
     ACCGCTGT

and it occurs at a 1-based offset into the sequence of 6
[download]

The bits you are probably interested in are

1. The bit to extract the overlap:

   substr $s1[2], $s2[ 1 ] - $s1[ 1 ], length( $s1[2] ) - $s1[1] - $s2[1]
   +;
   [download]

2. And the bit to calculate the 1-based offset:

   $s2[1] + 1;
   [download]

but they won't work correctly unless you split the input strings into their constituant parts and ensure that the first is the 'lesser' of the two.

It could undoubtedly be golfed some.