Looks like those green levers at either end of the CPU heatsink should be the key to removing it.
I've worked on a Dell PC with something like that before (many years ago) but I can't remember for certain how the levers worked now. I think you have to push the "ear" that sticks out of the clip toward the gap next to it so it kind of slides the shorter end of the clip out of the retaining mechanism.
Once you've got both of those out, you should be able to remove the heatsink.
You may find that the CPU sticks to the bottom of it, though - the thermal paste could well have set solid after all this time. I always used to try and make sure the system was fairly hot before removing the heatsink (if it worked and could run a CPU burner for a while) to soften up the paste. You could try twisting the heatsink a little in both directions repeatedly until it loosens up, if there's any slack in the mounting mechanism.