[AC Question]

Galaxy 5 and my samsung tablet without having to purchase other products.

[OceanView]

That's gonna depend on if the phone is GSM unlocked and if the NZ carriers support the frequency bands.
I would try to find out which bands are on your phone and then look at the carriers in NZ to see which bands they use.

[Tim1954]

If you use non new Zealand sim, you will be effectively roaming and you will get huge bill! I'd your device is unlocked, you can get a local sim. If not, there are ways to unlock it, your carrier can give you a code...