I dug around a little bit to see what I could find out, since I also play the black side of the Ruy, and I do play that move order generally. (Learning lots of theory was never my strong point!)
It turns out that 5... b5 is played a fair bit, but the follow up in top-level games is usually not 6... Be7, it's generally played with ideas of Bc5 or Bb7 instead.
All the same b5 followed by Be7 has been played a fair number of times as well, and it does not seem to be disastrous in any way. Most white players do in fact continue 7 Re1 transposing right back to the normal lines, but it looks like other things esp 7 d4 and 7 c3 are possible, and might possibly score better than Re1.
People have played b5 first against the likes of Fischer, Tal & Alekhine and come out with a draw, so it can't be that bad!
Ivanchuk played it against Shirov and won in this one...
http://www.chessgames.com/perl/chessgame?gid=1464697So it seems to be a reasonable move at least.