Rainy season? you're going to Spain not the Borneo. Their weather system is not dissimilar to the UK except scaled up in terms of temperature, so winters are mild/rainy/overcast and summers are darn hot. In May it will be getting into hot season so plenty suntan oil. Cheap flights: it all depends on where you're travelling from/to but some of the budget airlines (easyjet, jet2 etc...) can do returns from around �100. Or you can chance your arm and get a flight on the day for next to nothing. I trust you're looking online for flights?
http://www.monarch-airlines.com/
for example, can do Manchester to Alicante, return, 1 adult, flying 20th May (07:15) returning 27th May (20:50) for �75.70 which includes all airport taxes (the only downside is the unsocial flying times but you can pay a bit more for a better flight time).