I was given an iPhone 5 with a badly smashed screen for helping a friend with various Mac-related problems. Apple had said that the screen could not be fixed.
I bought both the new display assembly and some new screws for the bottom of the iPhone 5, and followed the instructions on the iFixit site to replace the screen. It all worked, but was definitely not easy, mostly due to the way the display assembly is attached to the case.
The main problem was that the suction cup could not get any grip on the screen because it was so badly damaged. Even putting clear packing tape over the screen didn't provide enough suction for the cup to hold in place, so it could not lift the assembly out of the case, as it would always break away first.
Finally I carefully broke more of the screen, and cleared away more of the glass, then levered the display assembly up with a spudger, taking great care not to damage any of the components underneath. Everything in the iPhone 5 is close together, so this was very difficult.
Once the new screen was on, it was relatively easy to get a good seal with the suction cup and lift it, though it takes a lot more force than you'd think. I did that a few times to make sure it could be done, and it's fine with an undamaged screen.
Put a thick piece of string around the suction cup to be able to pull on and get as much leverage as possible. Pull hard on the string to lift the display. It's the only way I could get the display to separate from the case, and the amount of force required is surprising. The suction cup I was given in the iFixit tool kit does not have the ring attached as shown in the pictures and video for this repair. Mine has a slot in the top part, and I used that to wrap the string around it so I could get the best leverage. I've put a couple of photos of the cup with string attached to show what I did. Getting the display assembly out of the case was the hardest part of this repair from my perspective.
When putting in the new display, it can be very hard to get the 3 cables attached, as they don't stay down on their contacts very well. I kept taking them off and repeating the process of putting them on, which I think helped the cables bend into shape better, so that eventually they stayed in place on the contacts on the phone. But it took several attempts, and none of the cables seemed to sit well at first. I can only advise patience and persistence, as in time they seem to improve, but be prepared to repeat the process over and over until you get them firmly seated. This part is really tricky, because these cables are fragile, so it's worth taking time to get it right so that everything works, as otherwise you'll put the phone back together, only to find the cables are not connected.
Due to the difficulty of getting the damaged screen out of the phone case, I'd say this repair is a lot harder than it has been rated on the iFixit site, at least for a first time effort. Once you've done it once, it becomes a lot easier.
Unlike the original Apple pentalobe screws for the bottom of the iPhone 5, the replacements from iFixit don't sit flush with the case. They project just a little, which to me is no problem as I have a rugged case over the whole thing, but if you don't have a case, the screw heads could catch on things. Also the replacement screws are not as long as the original Apple ones, but do seem long enough to do the job, if only just. If they could be made to sit flush with the case bottom, that might improve the length of screw available to go into the screw slots. But that may be very hard to achieve, and they certainly work as they are. I put a small amount of locktite on each screw to prevent them falling out.