macOS Sierra Public Beta 5 Update problem...not updating?

The public betas are up to version 6 now.

If you have trouble updating via the mac app store you can get the PB6 installer packages here and do it manually: https://forums.developer.apple.com/thread/60700

If you do it this way though be sure to follow the instructions properly. Some other people who just went there to get the installer packages, and not bother to follow the instructions carefully were unable to install the update via the packages.