temperature doesn't matter for sun. Summer solstice is 21st June which is the peak of the rays, so the UV is ramping up big time in May (it's a sine curve) and even if it is cloudy, you can still get burned.
sea and pool could still be a little cool, so the kids might prefer wetsuits - good to keep the sun off anyway.
I would guess it will be cool in the evening if planning to eat outdoors, so take cardi's/jackets. And you can't guarantee it will not rain. Over the past 10 years we've been to lots of places in the med in May and the locals have said that April used to be the rainy month, now it has extended into May and is unpredictable. Obviously this impacts on their trade, because people aren't hiring sunbeds on the beach or doing watersports, or spending money in bars and restaurants because they stay in their hotels when the weather is bad.