1)... Be7!  [It is the key move my good friend] 

2)Rxe7 Bf1
3)Rxf1 Rxh4 # if [3)Re6+ dxe6 ó  3)Rxh7+ Kxh7  In both cases it cannot be avoided 4)... Rxh4 #] 

2)Rf6+ Bxf6 if [2)Rxh7+ Kxh7] 

3)c8=D Rxh4+ if [3)Kg1 Bh3+ 4)Kf2 Bxh4 # ó 4)Kh2,Kh1 Rxh4 and it is impossible to prevent 5)... Bf1 #] 

4)Kg1 Rh1+
5)Kf2 Bh4 #
 
I think I did not miss an interesting variant. Teacher, I admire your prowess when playing and this problem was positionally amazing ...