Looks to me like a compatibility issue. You'll have to wait until Pioneer releases a software update. Also check your App Store and see if there's an update for AppRadio that might include a fix.
The real perk to iOS5 is better compatibility and the use of AppRadio extensions. Not to mention the native Maps app isn't completely effed like it is on iOS6. Teaches you not to be on the upgrade bandwagon looking at what they did to iOS6.
Remember that Advanced App Mode is a relatively new feature and the Video Out is intended for DVD viewing. I recommend in the future that you read the manual for a product before you buy to check for compatibility. Not trying to excuse the lack of this feature, but as with all products, there's a certain degree of buyer beware.