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use warnings;
use strict;
...
my @times2;

for my $elmt (@times) {

    if (! @times1 || $elmt - $times1[-1] >= 10) {
        push @times1, $elmt;
        next;
    }

    if (! @times2 || $elmt - $times2[-1] >= 10) {
        push @times2, $elmt;
        next;
    }

    push @times1, $elmt;
}

print "Times1: @times1\n";
print "Times2: @times2\n";

Times1: 5 20 30 40 50 65 75 90
Times2: 10 25 45 55 80