why is the app store for my iPhone 5 not working?

Try these things.

Go to Settings>General>Date and Time>Set Automatically>Off. Set the date one year ahead. Try to update the apps again. If you get an error message, go back to the settings. Correct the date and time (set automatically) then go back and try to update the apps again.

Or try this

Settings>Privacy>Location Services>System Services (swipe to the bottom of the page to find this)>Location Based iAds>Off.

I have the same problem for 2 days now

I have had the issue for several days as well. Tried Ocean's suggestions and it didn't work for me.