Hi, Jane,
I will be walking the Camino del Norte while you're on the Frances. So I wish you a Buen Camino!
Last year, on May 15 or thereabouts, I FROZE in the Roncesvalles refugio with a lightweight sleeping bag and all my clothes, including rain pants. But that was the only night I was cold (and I had started in Moissac, France so I had been walking for a couple of weeks before Roncesvalles).
In many places further along the camino, I think a down sleeping bag will be too hot in May. If you have access to something in between a down bag and a silk liner, that might be perfect, but if not, it's a choice between being warm enough all the time and hot sometime on the one hand, and being cold maybe once or twice and being fine the rest of the time.
I have a snugpak 750, and my husband uses a lightweight REI pack that was about $80 and we're usually fine.
Many of the albergues have blankets available, too.
Buen camino!