Razorback DBC

Can you get to the small spade slam with 20 HCP? We didn't. Partner held: J 10 8 6 3 2 AKQ x x Void x x I held: A 9 7 5 4 7 J 9 8 7 5 A J Partner dealt and opened 1S. Then: 2D, 2H, 3C, 4H, 4S, all pass. The K and Q dropped under the Ace, making seven I should splinter 4H. This shows a singleton or void in hearts, good spade support, and game-going values. [This was only the second time we had played together and I worried that he might not catch it. I should have splintered anyway and if it did not work, mark it up as a learning experience.] Then what should he do over 4H? I think 4S is his correct bid. Then do you think he should bid 6S if I bid 5C over 4S? Should I bid 5C? I would appreciate your thoughts.