I've spent waaay to much time thinking about this over the past few years and have really gotten into knots.
Personally I'd say you need to classify the type of knots you want to learn and pick one knot from each. The classics in my opinion are
1. End loop
2. Mid loop
3. Hitch (opposite of an end loop)
4. adjustable loop
5. Bend (rope to rope)
My suggestions in order are
# End Loop
1a. Bowline (snap variant) - This is a knot that's super easy to tie, remember, and untie. There are a bunch of variants to expand it's usefulness (double, water, slip, yosemite, etc)
1b. Zeppelin Loop - this is my personal favorite, it's a little tricky to tie but I've never seen it slip and it unties easily after it's all done.
# Mid Loop
2a. Alpine Butterfly - learn the butterfly method and this is an easy to tie knot that can be easily sized. It also doesn't bind so it unties easily and can be loaded in any direction (on of the only midline knots this is true for)
2b. Bowline on a Bight - Super satisfying knot to tie, a little wonky to learn just because of the structure but easy to tie once you get it.
# Hitch
3a. Tensionless Hitch - (this is probably the most overlooked 'knot' just look at a diagram you can learn it and never forget it after seeing the diagram once. It's the strongest knot there is if you have the rope for it. (I wouldn't really count this at one of your 5 but it's good to keep in mind)
3b. Buntline Hitch - dead simple and you can usually untie it after a heavy load
3c. Siberian Hitch - This is effectively a slipped noose but I use it all the time, it's my personal go to.
3c. Poachers knot - If you have a carabiner or know you're never going to need to untie this knot it's hard to beat
# Adjustable Loop / Friction Hitch
4a. Adjustable Grip Hitch - Easy to learn and holds better than the Midshipman's
4b. Midshipman - it's a little more complicated but this was Ashley's favorite because it can be tied under tension
# Bend
(Bends and fixed loops usually have the same structure so you might not need this one)
5a. Zeppelin Bend - seriously just learn this one, sixty nine method is the easiest for me. Knot is easy to tie, doesn't slip, and is easy to untie.
5b. Sheet Bend - this knot... is fine but you already know it if you learned the bowline above as it's the same structure
Bonus Section
1. Trucker/Truckee - probably one of the most useful knots around, learn the method that uses a slip knot for the mid loop and it'll make even easier
2. Canadian Jam Knot - Useful for bundling things, it's a knot I find myself using a lot
3. Voodoo Hitch - You can use it in place of a ratchet strap if you have a couple of carabiners
4. Icicle Hitch - Ever wanted to tie a rope to a butter metal pole and keep it from slipping? This is the knot, it cinches and grips things with so much friction you can tie a rope to about anything vaguely cylindrical