Should you remove recent apps from multitasking drawer? I own Nexus 5 with 5.0.1 Lollipop in it. I was wondering weather or not it is beneficial to remove recently opened apps from multitasking drawer or is it harmful for battery life and maybe performance?
What exactly happens when you remove recently opened app from multitasking drawer?
If you remove an app from the multitasking drawer it's marked to be closed very soon (just a few seconds) and it's memory is cached (instead of used).
This releases used RAM and prevents Android from closing running applications if another one needs more memory.
Depending on what applications you close with the multitasking drawer they will eventually restart (if a service is running in the background and launches the application again eg. Facebook) or they will just be closed.

Performance wise it's not a problem, applications you have closed might just take half a second longer to load up but that's it.
Battery life can be improved a little bit if you close down applications that would else run in the background and do some weird stuff that causes your battery to be drained quicker than usual.

Also: I'm not the best in understanding how the Android LMK (low-memory killer) works but it first uses available RAM instead of closing applications.