MSPATH nailed the "correct" reply above.
In May, along the
Camino Frances you can still hit snow at elevations over 700 meters. Expect rain. Plan for it. Also, morning temperatures in the single digits (c) are not uncommon. Albergues are frequently not heated. So, if you plan to stay in albergues, take a sleeping bag, at least a lightweight one. Search on the Forum for recommendations and tips.
As MSPATH states (paraphrasing) if you plan to stay in private albergues, hostals or hotels, bedding is typically provided. I have found that the more you pay, going up the continuum from albergue to hotel... the more you get. I have stayed in private hostals that provide a "blast" of heat in the radiators at 2200, and one other at about 0500, for an hour each time. Other places provided heat on demand - a luxury...
Currently, I am planning my fourth Camino for this April (so far). I am (finally) down to a rectangular, full zipper, microfiber sleeping bag liner from Alps Mountaineering. I stay in hostals or hotels 99% percent of the time, for personal, medical reasons...I learned in 2013 that my health was more valuable than the housing cost.
I usually only stay in an albergue if no commercial lodging cannot be found within a reasonable distance from my stopping place for the day. And then, I prefer a private albergue...it's a sanitation and communicable disease thing. I am a sponge for anything respiratory... So, needs must...
I recommend using
www.booking.com for locating commercial lodging. They feature inexpensive private albergues, all the way up to paradors (5-star hotels). However, not ALL lodging options are represented.
Also, from May through September, you will be competing for advance, reservable space against organized and led tour groups, package tour groups, students on formal chaperoned programs, etc. So, continue to do your research, both on this Forum and the web. New places are always coming on line, and some older places sometimes drop off the scene...
Remember 2016 is a proclaimed "Jubilee Year" by the Catholic Church (the Pope made the proclamation). This factor will increase the load demand all along the Camino, especially the Frances. I twill not be as crowded as during a formal Hioly YEar, the next one coming in 2021. But it will be busier than last year. So, book early and confirm often. I use Google Translate and e-\mail to send e-mail in Spanish. Most places, even if they do not have a website of their own do have an e-mail account.
I hope this helps.