Adams (14-20)
Elk Hair Caddis (14-18)
ANTs (14-18)
Pheasant Tail Nymph (12-18)
Wooly Bugger (8-10)
San Juan Worm (16)
Honorable mention: Griffiths Gnat (16-22)
As a new fly fisher, I imagine you will want to do more dry fly fishing. The first 3 patterns will cover may flys, caddis, and terrestrials. I would definitely have ants, if you want to have an easy tie as well as catching a lot of fish on dry flies, that is. A PT nymph will usually be as effective as any other nymph. Tie them in all sizes. Wooly buggers will give you a good streamer, as well as another nymph pattern if you want to fish it as a nymph. And it will catch fish on days when you may have trouble catching them, as well as when the water is high after rains. And yeah, I know you only asked for 5, but San Juan Worms are so easy to tie it's ridiculous, and they often are about the easiest sub-surface fly for a newbie to catch fish with, that I had to add them to the list. And I added Griffith Gnats as a midge option, although very small Adams can also be used for midges.
As a new fly tier, these patterns will give you some experience at tieing a gamut of different styles and techniques, and they are fairly easy. You should also try tieing some parachute style Adams to learn this technique, as well as the fact that they work real well. If you don't want to tie all the sizes I gave, tie the middle sizes only. If you are going to tie a range of sizes for a particular fly, start with the larger sizes first, because it's easier to tie and learn the technique this way.
