Hey, I've just fixed a previously-thrown iPhone 5 with dead digitizer. The screen wasn't cracked, although it stopped detecting the touch.
What I did was the reflow using the kitchen oven.
First off, I've took the phone apart and took the logic board out using this tutorial: iPhone 5 Logic Board Replacement
(I didn't take the battery out, if you don't have proper tools or are scared of destroying the battery, you can leave it there)
Then, I've preheat the oven to just below 200 degree celsius
(around 385 Fahrenheit? We have a metric system here in Poland, so I'm not sure)
and put the board on the cardboard inside.
(Don't worry, the cardboard will not catch fire and the plastic connectors will not melt. Just don't go any higher with the temperature)
Leave it there for about 7 minutes, then turn the oven off and open the door
(The smell may be unpleasant)
Let it cool down with the oven for about an hour.
Then, after making sure the board is cold, you can re-assembly the device and power it on. Worked like a charm for me, so far after 5+ hours nothing seems to be wrong. It also fixed the problem with the camera, so it's a double win here.