I spend a lot of time in the Zirkels, but you will be there very early TBH. It’s just going to depend on the weather between now and then. I’ll give you some ideas, but I’m not sure you will be able to do any of this.
It’s hard to cover much ground there without traveling the Wyoming Trail (aka CDT). 5 nights is a pretty long time to spend there TBH. But hiking along the Wyoming Trail with side trips down into basins or valleys would probably be your best bet for a longer hike. So maybe you can just go up to the Buffalo Pass TH, which is on the south end of the wilderness, and head north and see how it goes. If it’s walkable, you can go down to the Elbert Lake/Porcupine Lake/Luna Lake/Lake of the Crags are on the west and explore there. You can also continue north on the Wyoming Trail and go off-trail down into the Wolverine Basin, which is very nice. I can tell you the route. North of that, you will need to go over Lost Ranger Peak, which could have a lot of snow, but it’s nice if it’s reasonably clear.
Alternatively, you could do the standard hike starting at Slavonia Trailhead on the west side and do an extended Zirkel Circle hike by heading up towards Red Dirt Pass. Depending on the conditions you can scramble up Mt Zirkel. You could extend that further by going over Ute Pass on the East side of the valley and camp at a lake below that.
There are also very nice trailheads on the East side that access lakes. The Rainbow Lake trail gives nice access to the Slide Lakes, Roxy Ann Lake, and of course Rainbow Lake. You could also do a loop connecting the Lake Katherine drainage to the Bear/Bighorn Lake drainage via Ute Pass. None of these will really be 5 nights. In principle you can do a big loop from one of these trails up to the divide, go south on the Wyoming Trail, then go down a different drainage (e.g. Red Canyon or Round Mountain Lake) and connect back by the Grizzly-Helena trail outside the wilderness. But that return will be really boring.
There is a nice disconnected area at the north part of the Wilderness that includes 7 Lakes and the Encampment river, etc. Again, I don’t really know how you make it into 5 nights.
Frankly, most of this could just be a fantasy in May. But feel free to contact me if you have questions or want more details.