Actually I do not have the exact key. My original solution was: 96,0,0,2,2, which I considered the key for a while. But several days before I got this "97" answer from my friend in US. I think it is the best plan.
The reasons are: Because when 4,5 left, 5 will definitely disagree with 4 to gain all the gems. Therefore, when 3,4,5 left, 3 will propose 100,0,0. No. 4 will agree with the plan to save his life. Therefore, when 2,3,4,5 left, 2 will propose 98,0,1,1, then 4 and 5 will agree with him. Therefore, at the beginning, No.1 will propose 97,0,1,0,2, then 3 and 5 will agree with him, meanwhile he can maximize his benefit.
Very interesting in analyzing the whole situation.