We have a condo out in the mountains. May is not going to work - snow isn't gone.
Also very key to acclimate to altitude. Part of that is hydrating heavily until you're peeing clear before you even leave. That generally takes most people a week or so. Then, out there, you pretty much better have water bottle on you all the time and recommend some sort of electrolyte additive. Once you get dehydrated it is really hard to catch back up. Generally takes me an out 5 days to acclimate to around 7500' starting from about 700'. Cycling above that is going to take a few more days and you'll need to spend some more time at altitude to get there.