First thing first Playstation 3 error 80028EA5 is an UNKNOWN ERROR, and it is typically a connection issue that will not allow PS3 owners to sign in. One interesting thing about this PS3 error 80028EA5 is that it occurs mostly during gamer's gameplay session, logg off, and then when times comes to reconnet, the error code appears along with a message "You have been signed out of PlayStation 3 network (80028EA5)".
Based on the research on this type of unknow errors, following may be one of the cause of PS3 error 80028EA5.
The best possible solution for PS3 error 80028EA5 is to wait it out. Try to reconnect occasionally and see whether the problem gets resolves itself. Also try to contact other gamers or friends of yours and cross check whether they too are experiencing the same issue. If yes, then its a network issue and which you will not be able to resolve by troubleshooting your PS3.
If same issue persists for more than a day, directly contact SONY CUSTOMER CARE SUPPORT to know the actual cause of the issue, and the time period it will take to resolve.
There's one good and one bad thing about this unknow error 80028EA5. The good thing is the error is not cause by any fault of yours, and its not a serious one that will affect your PS3. The bad thing is that you can't do anything to resolve the issue.