There is currently no option to log chats like in Teamspeak 3. When a chat is closed (e.g. by a client disconnecting), the chat won't get opened again when the client reconnects or messages you again. Old messaged are not contained in the new chat, they are just plain lost.
It would also be nice if there was an option to open old chats without the client being online. There is a plugin for this called "Chatlog Viewer" for Teamspeak 3. I would really appreciate to see something similar integrated into Teamspeak 5.

Also just wanted to say thank you for the awesome work on Teamspeak 5 so far! Despite the missing features (obviously, it's a beta) everything looks extremely good so far