IMO it should basically be a scaled down PS4, using an AMD APU with around 1/10th the performance of PS4's processor, definitely possible with the latest AMD mobile processing tech to run on a mobile battery.
1GB unified memory at 30-40GB/s would be more than ample.
Memory storage built in, if an iPod classic can have a 120GB HDD then a modern handheld console should be able to as well, failing that 32-64GBs of solid state storage.
For the controller it should have the same button layout, analog sticks, D-Pad and Triggers as the Dualshock 4, only instead of the touchpad the touchscreen in it's place.
The system should have 2 SD Card ports, one for games, the other for extra storage.
There should also be a HDMI port (micro, with a micro to big HDMI cable in the box) for streaming gameplay.
Latest USB port for charging and physical data transfer.
Direct bluetooth or faster data streaming to allow for streaming second screen PS3, PS4 and PS5 gameplay and playing all of those games mobile on the unit (simple Wifi feature too for when you're away from your consoles).
Should use a version of PS4's OS and API, so developers can easily scale their game engines to run on the system.
System should have full support from AAA 1st party developers and studios external to Sony.
