Such a shame that Graph is out of support.

use 5.16.2;
use warnings;

use Graph;

my $g = Graph->new;

while (<DATA>) {
    $g->add_edge (m/(\w+)/g);
    }

say join "-" => $g->SP_Dijkstra (1, 5);
__END__
5 6
1 2
2 3
2 4
4 5
1 3
3 5

->

1-3-5
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