Hi, Deborah,
Welcome to the forum!
I don't think booking ahead is necessary at all. May is a popular month on the Vdlp, but all the albergues and private places will be open. In any town where there's likely to be a crunch, I think you will easily find private alternatives if the albergue is full. For instance, when I walked a few years ago, I spent several hours visiting the Roman city of Itálica. That meant I arrived in Guillena in mid afternoon. The albergue was full, but the nearby Bar Francés has rooms and it wasn't a problem. I think that the numbers of walkers on the Vdlp are generally still in line with the availability of accommodation. I haven't been between Sevilla and Zamora for a few years, but last year I joined the Vdlp/Sanabrés in Zamora and from there north there were no problems with accommodation and we never worried about reserving. I left Valencia in early May, which means I joined the Sanabrés at about the same time you will join it.
The one exception I would make is that if you are going to try to stay at the Hostal Asturias near the Arco de Caparra (lots of information on this stage here on the forum, but ask if you have questions). If you want someone to come pick you up, you'll need to call the day before.
Not having to worry about booking ahead is a great relief on the Vdlp because there are several places where you option is either 18 or 34 kms for the day (or something like that) and it's frequently impossible to predict which you'll feel like doing until you get to the first potential stopping place.
Buen camino, you´ll love the Vdlp! Laurie