I could do this with just one band, and do it twice:
Hall & Oates (greatest duo of all time, no question and fully objectively), songs in no particular order:
Say it isn't so
Adult Education (Rock & Soul Part 1 Album Version)
She's Gone (Rock & Soul Part 1 Album Version)
Some Things are Better Left Unsaid
You Make My Dreams Come True
(yes I skipped Private Eyes and Maneater, they are great songs and were radio mainstays, but I felt the above songs were better, objectively)
Monster Magnet (greatest metal band of all time, no question and fully objectively - pioneers of stoner rock and psychedelic/space metal), songs in no particular order:
Bummer
Look to Your Orb for the Warning
Cry
Silver Future
Space Lord
(again I skipped the few songs they had that got some radio play, such as Monolithic and God Says No, but I did include Space Lord because it just rocks hard and has a hell of an awesome story. The only good time I had when I did my ketamine infusions was listening to Powertrip the album straight through, my God did it invoke some seriously awesome visuals. That album is worth a straight listen through no matter what, on a CD format, because they tie the whole album together through sound effects a little like Dark Side of the Moon and a few other 70's/80's albums. I think Dio had one that did this too. Can't remember exactly. But, yeah)
I could choose either list above for the rest of my life and be happy with my choice.
To tie it down to just 5 songs total will take some serious thought. I tried to go that route and continually kept changing the list as I thought of other great songs and was like "oh yeah, I forgot that one" and so it went around and around. I will give it a try later.