Connect your iPhone to your computer and back it up using iTunes.
When connected, iTunes will download from the iTunes store all the purchased apps, free or not, to you PC.
Still in iTunes, with the phone connected and selected, explore the tabs until you find the one that allows you to remove apps from the phone.
Those deleted apps will still be in iTunes on your computer and can be put back on the phone at any time.
Hope that helps
My iphone 5 is running out of room to download any Apps or puting music into the phone. I downloaded a lot of games since they were free for a limited time; a lot of those I haven't even touched yet. I was wondering if there is a way to to delete the game from my iphone, but keep keep the game later to install again without purchasing it. I also wanted to know that if I deleted a game, I would keep a save file so I won't have to start all over in Final Fantasy ll or Infinity Blade. I'm a computer saavy so I'm unsure how my iPhone fully works.