Iphone i5 can't use App Store or load updates

I bought my iphone i5 about 2 months ago. I've been using iPhone for 4 years, and I use 2 iphones now, a 4s 64GB and a 5 32 GB. It is important because I can compare the 2 iphones on the same wifi etc.

When I bought my i5, I immediately noticed that it does not seem to be faster than the 4s, but it worked. Then I started experiencing problems with the i5 while using wifi. Then, since about 2-3 weeks ago, I have started experiencing problems with the i5 while using any kind of internet connection, does not matter if it's wifi or 3G. Very serious problems, I mean it is like I can't download my emails, can't browse on the Safari app, Facebook app sometimes working, sometimes not, Youtube sometimes working, sometimes not, the only app that seems to be stable and reliable is a GPS-based sports app, Sports Tracker.

I can't even use the App Store! It can't load the updates! ****.

My software is up to date, I tried shooting out and restarting the apps, tried restarting the phone, etc. No improvement.

My boss, who bought his i5 the same time as me, has been experiencing the same problems. One interesting fact, that he also can't use his iphone for browsing etc., but he tried using it as a hot spot, and it worked perfectly as a hot spot, it shot the internet to the iPad like it is a perfect router!

THIS IS SERIOUS. I bought my i5 for a lot of money, and I can't use it for internet browsing. My boss also can't.

Should I wait for some software update, or should I bring my i5 back to Apple, and ask for a new one?!?!

please HELP!