The problem may not be the fuse itself, but rather other parts of that circuit. The trick of course is figuring out exactly what.
One end of the fuse is the power source, and the other end has the loads. Since multiple devices go wacky when the problem occurs, it would appear the problem is upstream of where the loads fan out, which I think is right at the fuse block. That leaves the power and connections coming into the other side of the fuse, the fuse and contacts, and the connection for the loads.
Have you confirmed that nothing on any of the other circuits are failing at the same time? Fuse 5 is switched by the ignition switch, along with some others. If others are failing too (which may be less obvious), then the problem may be in the ignition switch. For example, does the fuel pump stop? That could be related to both the stall and re-start problems.
You might try measuring the resistance between the fuse contacts with the fuse installed. See what you get, and twiddle the fuse to see if the measurement is stable or if it jumps around. It sounds like you've cleaned and checked this section, but you never know....
If possible, check all the connections behind the fuse block to be sure they are tight, not corroded, and that the wires are not deteriorated.
You might also prepare yourself for further diagnostics the next time the problem happens. Catching it in the act is probably your best bet for nailing what's happening. If you carry a Volt meter or test light, you can check things the next time it happens, assuming you are in a place where it can be done safely. If you get the opportunity, here are some things to check. Don't shut off the ignition. Just park and pop the hood.
- Listen to whether the fuel pump is running. If not, the problem extends beyond fuse 5.
- Measure the voltage on both sides of fuse 5. There should be 13V on both sides. If you only get it on one side then you have a bad fuse and/or fuse contacts.
- Measure the voltage on both sides of another switched fuse (#4 is the fuel pump and would be a good choice). There should be 13V on both sides, and the results should correlate with listening to the fuel pump.
- Measure the voltage on both sides of an unswitched fuse. There should be 13V on both sides. If not then you have a more fundamental power problem, but at that point it's a short list of places to look.
Let us know what you find.