I have wrote a program that stores five numbers in different variables

This is the part which is confusing. You clearly know how to use arrays so why not start with an array?

my @nums = (5, 10, 15, 20, 25);
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That way your sum could be written:

my $totalSum = 0;
$totalSum += $_ for @nums;
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or alternatively

use List::Util 'sum';
my $totalSum = sum @nums;
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And your final array assignment could become

my @array = map { $_ / $totalSum } @nums;
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By starting off with separate scalars, everything you do becomes repetitive. It's feasible for 5 numbers, but what about 30? or 100? or 1000000?

The other thing I would change is to remove the -w from the first line. Using warnings as you have done is better as it gives lexical scope and finer control where needed. The -w negates all that.