Conditions in May are like you describe; colder but with solid snow bridges and such. Weather in May, however, is still very much a crap shoot. The weather can be localized and Rainier is like a magnet for storms. You can plan for anytime in May, but to improve your chances plan as long a trip as possible and 'chase' the weather be it alpine climbing in the Enchantments or rock climbing in the desert until the weather on Rainier is good enough for an attempt. Also, be aware that in May the only likely viable approach will be via the south side/Paradise so plan your route accordingly.