You must take off the heatsink prior to cpu removal.
Post pictures so we can better visualize where you are in the removal process.
Below is a photo showing the 2nd to last step. Cooler/heatsink is already removed, you need to use the level thing to lift the bracket that holds the cpu down, then the cpu is easily pulled out. Each mono/cpu combo will be semi specific but the overall is the same
Thank you. Yes, I know this, I put the PC together, so I know all the steps you describe here.
Thing is I can't post a picture right now, cause the PC is assembled and in the case, but I might want to take it off soon. You can look up the motherboard, MSI B650 WIFI Gaming Plus.
When I do all this (and this is when I wanted to take it off back then), I can't really grab the sides of the CPU, the CPU is in the hole in the socket, surrounded by the socket.
I thought am5 CPUs usually have big notches in the top part, seems like it should be easy enough to grab on to those.
Otherwise, there's usually enough space around the sides that you can fit a fingernail/toothpick/tweezers in there and flip it out. You could also put your hand over it and flip the whole thing over.
So the top part, the "heatsink" part, I can grab it by that, but the grip is bad and I can't take it out (at least not without rapidly grabbing it and pulling it to the side out of the socket), and I don't want to touch those electronics under it (as shown in your picture).
I can't really grab it by the sides with fingers, I could perhaps with tweezers, but too afraid those could scratch something in the process.
A small suction cup might work as someone else mentioned though, but don't have that.
Those are just capacitors or resistors, you can touch them they don't care. As long as you don't have a high static electricity charge on you you can freely touch anything you want in the computer. Touch any part of the case before you start working on it and you're good.
Just maybe don't touch the pins under the CPU since they're really delicate. But anything else touch to your hearts content. Computers aren't that fragile. Also this: https://i.imgur.com/qD1bHtE.jpeg
A couple of questions.
What CPU do you have?
Have you taken the cooler off yet? It sounds like you haven’t, and that’s a pretty important first step. I recommend running the computer for a little bit to get the cpu up to temperature to soften the thermal paste before trying to remove it. Most CPU coolers are either screwed or latched in place.
Once the cooler is off what exactly you’re looking at will vary slightly between which CPU socket you have. Most have a little round rod/lever that runs along the side of the socket that will need to be lifted before the cpu can be removed. It should come out easily
Well, I kinda am not trying to take the CPU out right now, but last time I tried I faced this issue (as well as when trying to put in, I just had to sorta drop it from a bit above), and I might want to take it out again soon.
The cooler/heatsink is removed in this case, by heatsink in the OP I mean, the like metal thing on top of CPU, the thing you put thermal paste on, not the actual heatsink you put on the CPU, but the shield thingy attached to the CPU.
There should be a gap on one side of the socket where you can lift from, as seen on the left side of this pic. Disregard the red circle, this is from a messed up pin post lol 
Ah, I didn't know this, thank you. I can try from this when I want to remove it and see how it goes.
