May can have any weather from cold and snowy to hot and warm. It tends to rain a lot in May. I have camped there then, and early June is not always much more or any more predictable. Waters can be high during this time of year...not sure what you are planning to do, but much of Yellowstone the first week of May will look like Winter.
We did the first week of June last year and it worked well for us. There was still snow in the mountains but the temp was fine.
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