my iPhone 5 having trouble receiving certain calls

I Just recently got my iphone 5 for christmas and have been loving it. However, recently I have not been recieving certain calls or texts.  People tell me that they called me or texted me at a certain time.  When I check in my recents it shows nothing, or even on my texts.  Then sometimes, it shows the calls or texts from 3 to even a day after the call or text is sent.  I am very angry and expect my newly purchased iphone to be fully functional.