Q: iPhone

Hello elianeh,

Congratulations on your new iPhone!  Also, thank you for the details of the issue you are experiencing with the App Store on your iPhone 5s.  For this issue, I recommend signing out and back into the iTunes Store on your iPhone:

Changing your Apple ID account

Tap Settings > iTunes & App Stores, then tap the Apple ID signed in.

Sign out of the current Apple ID account and then sign in with another account or create a new Apple ID.

The last step states to sign in with another account, but for the situation you described, I recommend just signing in with your same Apple ID.

You can find the full article here:

iOS: Changing the signed-in iTunes Store Apple ID account

http://support.apple.com/kb/HT1311

If the issue persists after signing out and back in, I recommend quitting and relaunching the applications on your iPhone:

1. Double-click the Home button.
2. Swipe left or right until you have located the app you wish to close.
3. Swipe the app up to close it.

You can find the full article here:

iOS: Force an app to close
http://support.apple.com/kb/ht5137

If you are still seeing the same issue after quitting and relaunching the iTunes Store app, I recommend restarting your phone and then resetting if it's still not working:

Restarting your device

1. Press and hold the Sleep/Wake button for a few seconds until the red "slide to power off" slider appears, and then slide the slider.
2. Press and hold the Sleep/Wake button until the Apple logo appears.

Note: Reset your device only if you are unable to restart it.

 

Resetting your device

Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.

You can find the full article here:

iPhone, iPad, iPod touch: Turning off and on (restarting) and resetting

http://support.apple.com/kb/ht1430

Thank you for using Apple Support Communities.

Best,

Sheila M.