It says on my profile that I am using 10 slots out of 6. If I upgrade my account and want more, am I going to have to buy 5 slots to get another pet? This just seemed odd.

If you activate a gold account, it'll give you 5 more slots, so you'll be able to get an 11th pet. But if you wanted a 12th pet, you'd have to buy another slot (bringing you to 7 normal) and then activate a gold account (bringing you to 12) to fill it.

Oh I understand now. Thank you :)

You also can get pet slots from loyalty boxes but you still need a GA to actually fill them. c: