The server network address “TCP://SQLServer:5022” can not be reached or does not exist.

Thanks to Pinal Dave:

Fix/WorkAround/Solution: Try all the suggestions one by one.

Suggestion 1: Make sure that on Mirror Server the database is restored with NO RECOVERY option (This is the most common problem).

Suggestion 2: Make sure that from Principal the latest LOG backup is restored to mirror server. (Attempt this one more time even though the full backup has been restored recently).

Suggestion 3: Check if you can telnet to your ports using command TELNET ServerName Ports like “telnet SQLServerName 5023”.

Suggestion 4: Make sure your firewall is turned off.

Suggestion 5: Verify that the endpoints are started on the partners by using the state or state_desc column the of the sys.database_mirroring_endpoints catalog view. You can start end point by executing an ALTER ENDPOINT statement.

Suggestion 6: Try the following command as one of the last options.

GRANT CONNECT ON ENDPOINT::Mirroring TO ALL

Suggestion 7: Delete the end points and recreate them.

Thanks : http://blog.sqlauthority.com/2010/01/11/the-server-network-address-tcpsqlserver5023-can-not-be-reached-or-does-not-exist-check-the-network-address-name-and-that-the-ports-for-the-local-and-remote-endpoints-are-operational-microso/