Add two vectors modulo 5
Python, score=215 166 (167 118 chars, at most 48 ops)

def A(x,y,z,p,q,r):
 u,c=x^p,x&amp;p;v,d=y^q^c,y&amp;q|y&amp;c|q&amp;c;w,e=z^r^d,z&amp;r|z&amp;d|r&amp;d
 if e:u,v,w=A(e,e,0,u,v,w)
 return u,v,w


Does addition in bit-parallel.  The c,d,e are the 32 carries from one position to the next.  e represents multiples of 8 that carry out of the vector, so if e has any bits set in it, we add 8%5=3 back in using a recursive call.

The translation table is the same as the one given in the question.