The strakes were indeed to make the spin less oscillatory in yaw.
Apart from the 5, I also flew the 167 Strikemaster for five years.
This too had strakes and was always flown with tip tanks. I can't remember the fuel figures for the 5, but when spinning the 167 the tip tanks had to be empty because of the relatively high B/A ratio.
Incidentally, we also flew it with drop tanks plus tip tanks full - in temperatures of 45C+, it needed about 6000ft of runway to get airborne!!
Mind you, once it was airborne, it went a very long way.
JP