Yes the 5/i battery and the 6/i battery are interchangeable. I tried the 5/i battery on a 6/i myself, and it worked fine. It helped me troubleshoot that my 5/i was unable to use a BBU. The batteries themselves are almost exactly the same, the 6/i batteries being a bit newer and with a different model number. Some say the 6/i batteries last a little longer, could be true (theoretically since the chemistry of the batteries would be newer since the 6/i is a newer part, it could mean the batteries themselves are newer than the 5/i ones which could have been manufactured long ago, especially if you buy the cards used) but there hasn't been any definitive proof (show me the numbers!).
The only area you may have an issue is if you try using a 5/e or 6/e battery on the 5/i or 6/i. Some people have tried using these combinations in this thread before and reported the battery was not recognized.