Can I take my unlocked iPhone 5 to t-mobile?

Can I get service with them?

As long as it is unlock

Yes.

No 3G or 4G data, No Siri unless on Wi-Fi. MMS rarely works and texts are spotty at best.

Of course, you will.

T-Mobile operates on HSPA+ for its 4G speed at 1700/2100 which is not supported currently on any of the iPhone 5s out there. For this reason, you are usually limited to 2G/EDGE speeds. But, T-Mobile has been refarming its network to use a LTE band at 1900 mhz. This is the news you have been waiting for, as this will allow iPhone users to experience 3G and 4G/LTE speeds and all functions of your unlocked iPhone 5 will become available to you. T-Mobile says the upgrade will reach 200 million people by the end of 2013, and you can check http://www.airportal.de/ to see if your city has already been upgraded.

Yes without a problem