finding the similarity transform connecting two sets of matrices

Question

Given two set A and B of matrices containing 5 elements. For example:

       A                      B
 1     0     0          1     0     0
 0     1     0          0     1     0
 0     0     1          0     0     1

-1    -1    -1          0     1     0
 0     1     0          1     0     0
 0     0     1          0     0     1

-1     0     0         -1     0     0
 0    -1     0          0    -1     0
 0     0    -1          0     0    -1

-1     0     0          0     1     0
 0     0    -1          1     0     0
 0    -1     0          0     0    -1

-1    -1    -1         -1     0     0
 0     0     1          0     0     1
 1     0     0          0    -1     0     

How can a unique similarity transform be found which maps each matrix in A onto the corresponding matrix in B. In other words, is there an efficient algorithm/method capable of finding $S$ such that $$S A_i S^{-1} = B_i $$ for every i.