use strict;
use warnings;
my $str = 'command1 command2 command3 "command4 --some-arg arg --some-
+other-arg 2" command5';


for (split m{(\s+|"[^"]*")}, $str) {
    print $_, $/;
}
[download]

That works, but produces a few strings that only contain whitespaces - you can filter them in a separate pass, for example with grep.

The other solution is match your desired output, not the delimiter.

Update: version with filtering:

use strict;
use warnings;
my $str = 'command1 command2 command3 "command4 --some-arg arg --some-
+other-arg 2" command5';

for (split m{(\s+|"[^"]*")}, $str) {
    next if m/^\s/;
    next unless length $_;
    print "<$_>\n";
}
[download]