How to apply Arctic Silver 5 thermal paste?

I only paste it on desktop CPU, I think it doesn't matter which method you use.
Just remember, don't apply too much thermal paste.

Liberally across both nipples. Keeps them cool in the summer.

How you apply it doesn't matter, as long as you get a thin spread between your CPU and the cooler. I use a very thin line of paste down one side, and spread it back and forth across the CPU surface until it's near paper-thin, using a razor blade to do so..

But really, there's no significant temperature difference between all the methods you've mentioned.

The pea-dot method is what I've always used, but it doesn't really matter as long as you don't apply too much, or too little you'll be fine.

I would go with surface spread, an uniform layer made with a plastic card. I remember using pea dot method on an old laptop and didn't worked at all. I also did the surface method with an AMD APU laptop and worked well. Or research even more.

As others have stated, it really doesn't matter how you apply it, as long as you cover the entire surface area of the die. Ideally you want it as thin as possible, but if you use too much, the mounting pressure should push most of it out the sides. I like to use a little more than I think is necessary and then push the heatsink down with a decent amount of force (don't break it), and wiggle the heatsink around a tiny bit for a while to help spread the thermal compound and push out any excess (you probably won't be able to do this with a laptop heatsink). Then I bolt it down. Just make sure not to move the heatsink too far or pull the heatsink off after you applied the thermal compound or else you can create air bubbles in it and air is horrible at transferring heat.

Just download a program to check your CPU temps and check them before and after to get an idea of how good it is applied. I like to use RealTemp, but there are other programs. If your temps are higher after you replace it, you screwed up somehow and you need to redo it. If they are lower, be happy :)

If you have no idea what temps you should be aiming for, you can look up online and see what temps other people are reporting on your same laptop to see if you are in the right ballpark. You want full load temps though, idle won't tell you much.

If it is a small chip, a pea sized dot in the middle is probably fine. If it is a bigger chip, like my GTX 580 that I just did, I used a bit bigger than a pea sized blob in the middle and then 4 lines going out diagonally to each corner from the center. Just do whatever you think will get it covered. You can also just spread a thin layer across the surface with something like a credit card. If you are going to spread a thin layer and the heatsink is flat and smooth, I would just cover the CPU die. If it is a crappy heatsink with grooves, like between heatpipes and is not perfectly flat where it contacts the die, I would spread the thermal compound on the heatsink so it fills the gaps.

You may want to watch these videos. They will show you that it really doesn't matter and people put too much thought into it.
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Linus Tech Tips

I always use the pea dot method, I've heard spreading can cause bubbles but either is probably fine. And ideally you probably want less than a pea size, it' doesn't take much.

Method doesn't matter that much. Ideal is not to have too much or too little. You want enough to just barely cover the surface, such that it can fill in the tiny gaps between the heatspreader and the heatsink. I like the line method myself (which works well provided you know which way the die is oriented), but you can also use any other method and it should be fine.

You'll want to be very careful with Arctic Silver 5 when applying directly to the die, while it isn't conductive, it is still slightly capacitive and as such you don't want to apply too much. If you do the heat sink could press it out and it could short something out. It might not damage your computer, but why risk it.

Screw the paste. Graphite thermal pads are the future https://www.youtube.com/watch?v=YpphKzmDiJM