First, are you sure you've accurately transcribed the code you are running? If I run

#!/usr/bin/perl -w
use strict;

my $runtime = 3600;
my $runtime2;
my $nextruntime = 0;

my $days = int($runtime / 86400);
$runtime -= ($days * 86400);
my $hours = int($runtime / 3600);
$runtime -= ($hours * 3600);
my $minutes = int($runtime / 60);
my $seconds = $runtime % 60;

$days = $days .'d ';
$hours = $hours .'h ';
$minutes = $minutes .'m ';
$runtime2 = $runtime;
$runtime2 = $days . $hours . $minutes . $seconds . 's';
if (time()>=$nextruntime){
        $nextruntime=time()+300;
        $runtime += 300;
        print "Duration: $runtime2\n";
}
[download]

I get the output

Duration: 0d 1h 0m 0s
[download]

which corresponds with your spec but not your cited output. However, on the next iteration of your loop, I would get

Duration: 0d 0h 5m 0s
[download]

This issue happens because you are dropping hour and above information on every iteration of your loop. You need to choose if you are going to destructively parse your term, or use it as an accumulator. You'll have better luck with something like:

#!/usr/bin/perl -w
use strict;

my $start = time();

while (1) {
    my $buffer = (time() - $start);
    ($buffer, my $seconds) = (int $buffer/60, $buffer % 60);
    ($buffer, my $minutes) = (int $buffer/60, $buffer % 60);
    ($buffer, my $hours)   = (int $buffer/24, $buffer % 24);
    my $days = $buffer;
    
    print "Duration: ${days}d ${hours}h ${minutes}m ${seconds}s\n";

    sleep (300);
}
[download]

As a side note, while(1) is incredibly abusive to system resources as you've implemented it. Take a look at sleep for implementing waiting in a script.