The really critical question when looking at parallel code is dependencies. I'm going to assume that - because your script can be subdivided - you're not doing anything complicated inside the loop.
But because you're stepping by 0.001 and 5 loops deep you're just doing a LOT of iterations if you were to go from 0 to 1. 100,000,000,000,000 of them, to be precise.
To parallelise, I would personally suggest you 'unroll' the outer loop and use Parallel::ForkManager.
E.g.
my $CPU_count = 256;
my $fork_manager = Parallel::ForkManager->new($CPU_count);
for ( my $k1 = $start; $k1 < $end; $k1 += 0.001 ) {
# Run outer loop in parallel
my $pid = $fork_manager->start and next;
for ( my $k2 = $start; $k2 < $end; $k2 += 0.01 ) {
for ( my $k3 = $start; $k3 < $end; $k3 += 0.001 ) {
for ( my $k4 = $start; $k4 < $end; $k4 += 0.001 ) {
for ( my $k5 = $start; $k5 < $end; $k5 += 0.001 ) {
...;
}
}
}
}
$fork_manager->end;
}
What this will do is - for each iteration of that 'outer' loop, fork your process and run the 4 inner loops as a separate process. It'll cap at 256 concurrent processes. You should match this to the number of CPUs you have available.
Bear in mind though - this only really works for trivial 'cpu intensive' tasks. If you're doing much disk IO or trying to share memory this won't work nearly as well.
Also note - if the number of steps on the outer loop is fewer than the number of CPUs it won't parallelise quite so well.
I'd also note - $k2 has a smaller iterator. I've copied that from your source, but it may be a typo.
&help any?