TLS protocol switching on F5

If you are talking about SSL bridging, as seems to be the case, F5 will terminate the SSL connection from the client and decrypt its traffic; then it will negotiate and set up another SSL connection with your application server, re-encrypt the client data and pass it to the application server.

There are two distinct network stacks on the F5, one for the client side and the other for the server side. The TLS protocol and cipher used by the connections on the client side and the server side can be the same or different; they depend on the capabilities of the two peers of each connection (client <> F5 and F5 <> application server). So how you configure the SSL profile for each side on the F5 is relevant. The highest/strongest TLS protocol/cipher will be selected by each connection after a sucessful SSL negotiation.