I don't know if your late May visit will extend into June, but June 4th is Pentecost Sunday, the day when the
Feria del Campo peaks. It's a
Romeria al Santuario de la Virgen del Rocio near
Almonte on the western border of the
Doñana wildlife refuge in the Province of
Huelva. The pilgrimage route (walking, riding decorated pony carts or on horseback) starts in Sevilla; so lodging in Sevilla may be very 'tight' that week.
It is definitely something to see! A million people (Police est. for 2002, last time I was there: 600,000), dressed in typical Andaluz costume ... playing Guitars and singing and dancing along the way