TLS protocol switching on F5

This is the selection sequence. You can reorder them by adding @speed or @strength.

0: 5 RC4-SHA 128 TLS1 Native RC4 SHA RSA 
1: 5 RC4-SHA 128 TLS1.2 Native RC4 SHA RSA 
2: 47 AES128-SHA 128 TLS1 Native AES SHA RSA 
3: 47 AES128-SHA 128 TLS1.2 Native AES SHA RSA 
4: 47 AES128-SHA 128 DTLS1 Native AES SHA RSA 
5: 53 AES256-SHA 256 TLS1 Native AES SHA RSA 
6: 53 AES256-SHA 256 TLS1.2 Native AES SHA RSA 
7: 53 AES256-SHA 256 DTLS1 Native AES SHA RSA 
8: 10 DES-CBC3-SHA 192 TLS1 Native DES SHA RSA 
9: 10 DES-CBC3-SHA 192 TLS1.2 Native DES SHA RSA 
10: 10 DES-CBC3-SHA 192 DTLS1 Native DES SHA RSA 
11: 60 AES128-SHA256 128 TLS1.2 Native AES SHA256 RSA 
12: 61 AES256-SHA256 256 TLS1.2 Native AES SHA256 RSA 
13: 9 DES-CBC-SHA 64 TLS1 Native DES SHA RSA 
14: 9 DES-CBC-SHA 64 TLS1.2 Native DES SHA RSA `

When it comes to clientssl the F5 controls the order of ciphers. When it comes to serverssl the application server controls it and not the F5. You see from the clients perspective the F5 is the server and from the server perspective the F5 is the client. They don't know anything about each other and there are completely separate network stacks for each of them.

The proxy SSL feature is when the F5 acts as specialised man in the middle. See the knowledge base article on the proxy SSL feature.