Cheryl, you will note that janettravels did not go to Barcelona. Crowds were much heavier at the Barcelona sites (early August) than at the Madrid sites in mid-May. I am very reluctant to say that you will have no problem in Barcelona if you wait till arrival to buy tickets, but having 5 days does help. Buying when you get to the city and have checked out the weather and learned about special events is not the same thing as walking up to the site and getting in line at the ticket office when you're ready to visit. You might get lucky once or twice, but you might end up standing in line for an hour or more. And in November the weather might be less than wonderful.
For sure the Palau de la Musica Catalana should be booked before you leave home if you don't want to take any chances and care about that site. The tours are not bi-lingual, and I assume you will need an English-language tour. This is not like the Alhambra situation, but people have missed this site for failure to pre-book the tour.
The Picasso Museum is bad enough that it is sometimes recommended that people book the Tourist Office's Picasso Tour because it ends at the museum and you have an hour or so on your own after the tour's walk-through. The website allows you to book a time-block now. It might be worth Googling to see what people have said recently about the line there.
When I checked with the Tourist Office early in my visit about how soon I needed to buy tickets for La Sagrada Familia and Parc Guell in order to get the first time slot, I was told two days ahead should be OK for LSF and one day ahead for PG. I do not promise that will work for you, but it did for me.
The T.O. sells tickets to most of the sites with problematic ticket lines. It does not handle Palau de la Musica Catalana tickets, and it does not sell tickets to the LSF towers. I bought the other tickets I needed at the Pl. Catalunya T.O. (which is underground), paying the 2-euro fee as a solo traveler for the convenience of not having to run around the city or worry about an e-receipt on my phone.
I did not ascend a tower at LSF, but there were some discussions here in 2016 about that experience; with luck the Search function will find them for you. You must choose which of the two towers you want to ascend.