Okay, I've double checked, and it is indeed:
5n/6^(n+1)
If there are n rerolls, the (n+1)th roll is the final roll. The probability of that in the simple exploding d6 case is 5/6^(n+1). The number of rerolls is the infinite sum of (number of rerolls times probability of that many rerolls) or 5n/6^(n+1).