This might be a bug in the beta 5 installer. I have the same problem trying to upgrade from Ventura beta 3 to beta 5. It downloads the beta 5 upgrade and restarts the Mac but never installs the new beta. I am running an M1 Mac Mini. BTW, can someone tell me how to install the Download Restore Image? It is an ipsw file and I can't figure out how to install it.

No work-around for me. I even tried reformatting my external drive and installing Monterey. Then tried the Ventura beta install with no luck.