Nobody can predict the weather, until its upon you. That time of year, you will likely get a mixed bag. Early on in the mountains, it could snow. Later on in May, it could be 25 C and sunny. Expect 5C in the mornings most of the way, warming up through the day to 15C or warmer most days. Up high near Cruz de Ferro or O Cebreiro, it could be quite cold and rainy. Oh yeah, and it will rain in Galicia. I just don't know how much!
Dress in layers. Make sure you can be comfortable with frost on the ground, but able to strip off layers as the day wears on, or add layers as the weather turns. When its cold, you're wearing everything you have in your pack, when its warm, all those layers go back in the pack.
Buen Camino