A simple threaded solution. Substitute your rsync commands for the sleep.pl:

#! perl -slw
use strict;
use threads;

for ( 1 .. 10 ) {
    async{
        my $secs = rand 10;
        system "sleep.pl $secs";
    };
    sleep 1 while threads->list(  threads::running ) > 5;
    $_->join for threads->list( threads::joinable );
}
sleep 1 while threads->list(  threads::running );
$_->join for threads->list( threads::joinable );
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