#1
I started bass earlier this year (well, last year I guess; it's 2015 now). I bought a Squier Affinity PJ bass because it seems pretty decent for the price. But some of the music I want to start practicing now is for five-string. Should I tune down to BEAD or should I get a set of BEADG strings and put those on it? It's been a few years since I restrung a guitar (I did classical and Spanish guitar for a while in college), but I think I remember how; but is it possible to fit thicker strings on there? What are the pros/cons of either option?
#2
I'd suggest taking it to a tech and asking if you can watch him/her do it. Changing the range so dramatically will need the setup altering, so that would be a good time to get that done too
#3
The biggest issue you will have is the nut slots not being large enough for BEAD. If you want to leave it step up as the low 4 of a 5 string you'll need to have the nut slots widened and the guitar setup. If you aren't planning on leaving it tuned that way I'd recommend not doing it as you can't really go back and forth that drastically on string gauges. Best bet is to pick up a 5 string or a second 4 to be at that tuning.
#4
The songs you're learning probably don't use all 5 strings at once, I would just try transposing the song up a 4th.
Unless you want to always be in BEAD tuning then you can set it up like that, but it will difficult to go back. You'll have to get it set up every time.
#5
Restringing an electric bass is probably a lot easier than is restringing a traditional Spanish classical guitar:

https://www.youtube.com/watch?v=-8uBYIwMevA

As others have said, throwing a .135" low "B" string on a four-string bass will probably not work, because the nut slot is not cut wide enough. You could down-tune your bass, but the strings might feel a little floppy.

Switching to a five-string bass is not a major undertaking as far as technique is concerned. Your biggest problem will be that you are so used to the top string being the "E" and now it will be the "B," so you will definitely hit a few bad notes. We all did it. You will adapt very quickly when you do get a proper five-string bass.
"Maybe this world is another planet's hell?" - Aldous Huxley