Can I activate a iphone 5 with a different SIM card?

I have a iphone 5c and i can't activate it without a tmobile SIM card. If i buy or use any SIM card would it activate even if the SIM card has no service?!

This solely depends upon if your phone was in fact factory unlocked or not? If your phone was factory unlocked for any GSM carrier, such as AT&T, T-mobile, Straight Talk, and so forth than yes you can use any SIM card to use on the phone, unless the phone was blacklisted or reported lost or stolen. If the phone however was once a Sprint or Verizon CDMA phone, it would have to be professionally unlocked before you may use it on any GSM carrier, as the mentioned ones above.

Hope this helps.

You can only activate your phone in the network you have purchase it. In your case, only a T-Mobile SIM card can activate your iPhone 5c.

Your 2nd question "if i buy or use any SIM card would it activate even if the SIM card has no service?!"

It can't. Because the iPhone 5c will only transmit its device ID through the network it is locked on, to the Apple servers. Then that network will send the needed data from the Apple servers to the iPhone for it to be activated. Unless it's unlocked, then any SIM will do.

So, if you want to use it on any network, better have it unlocked first.