Hmm...you do have to wait out the Spell's cooldown period before you attempt a subsequent summons, but you should see that interval counting down on the Spell icon in your Hotbar, if you have Hotkeyed the Spell. Initially, I thin it is about 15-20 seconds between casts.
You never get a simultaneous group of five skellies. You can get up to 5 active at the same time by casting the spell 5 times in sequence.
Your pet is actually better at this, when both heavily engaged enough to keep wanting more help and also healthy enough that he is not yet fleeing. Given the impetus to keep casting for more minions, the pet will of course time each successive cast precisely as soon as it is allowed.