While it's possible to install PS4 Fake PKGs (FPKGs) on Exploitable PlayStation 5 Consoles via the PS5 Kernel Exploit (3.xx-4.xx), unfortunately they currently won't run without a valid license (purchased games) or kernel patches according to @zecoxao on Twitter. 
For those recently joining the PS5 Scene, this comes following the Astro's Playroom (HDD PS5 ASTROBOOT) Updates, Robinson: The Journey PS4 on PS5 via NP-PS4AppCategory.txt Edit, Dumping PS5 PSN Games the Proper Way Guide, PS5 Kernel Exploit Payload.bin Loader Host, PS5 Hypervisor Exploitation from a PS4 Save Game and recent PS5 60FPS Patches via Editing Game Memory Demo.
Below is an image and video courtesy of @hyndrid on Twitter simply demonstrating the installation of PS4 FPKGs on PS5... although as stated above they won't launch, run nor play so it's primarily for show at this time.
Update: Since his previous updates, @tecniqueza confirmed on Twitter that the PS5 title Astro's Playroom V1.600 PKG (spoiler below) is both installable and playable using Exploited PS5 Consoles via the PlayStation 5 Kernel Exploit (3.xx-4.xx) as it utilizes a free license alongside a PS5 YouTube (PPSA01650) PKG (spoiler below) via @ifcompass on Twitter. 
Update #2: Recent Libhijacker Updates also allow games to launch now, but not play yet as they get stuck at a splash screen as confirmed by notnotzecoxao on Twitter... who stated, "it goes without saying this but, even if game loading does become a reality in the near future, there is the issue that sleirsgoevy payloads only decrypt PS5 demos and PS4 games correspondant to the PS4 *** version of 4.03 and below versions" going on to say "this means you won't have PS5 game loading from anything other than demos/freemium." 
Update #3: Developer @illusion0001 made available some PS5 Game Debug Menus with 60FPS PS5 Game Patches via his Libhijacker Github Fork as well now.
Update #4: PS5 4.03 HEN PS4 FPKG Enabler Payload & Porting Offsets by Sleirsgoevy!
For those recently joining the PS5 Scene, this comes following the Astro's Playroom (HDD PS5 ASTROBOOT) Updates, Robinson: The Journey PS4 on PS5 via NP-PS4AppCategory.txt Edit, Dumping PS5 PSN Games the Proper Way Guide, PS5 Kernel Exploit Payload.bin Loader Host, PS5 Hypervisor Exploitation from a PS4 Save Game and recent PS5 60FPS Patches via Editing Game Memory Demo.
Below is an image and video courtesy of @hyndrid on Twitter simply demonstrating the installation of PS4 FPKGs on PS5... although as stated above they won't launch, run nor play so it's primarily for show at this time.
Update: Since his previous updates, @tecniqueza confirmed on Twitter that the PS5 title Astro's Playroom V1.600 PKG (spoiler below) is both installable and playable using Exploited PS5 Consoles via the PlayStation 5 Kernel Exploit (3.xx-4.xx) as it utilizes a free license alongside a PS5 YouTube (PPSA01650) PKG (spoiler below) via @ifcompass on Twitter. Update #2: Recent Libhijacker Updates also allow games to launch now, but not play yet as they get stuck at a splash screen as confirmed by notnotzecoxao on Twitter... who stated, "it goes without saying this but, even if game loading does become a reality in the near future, there is the issue that sleirsgoevy payloads only decrypt PS5 demos and PS4 games correspondant to the PS4 *** version of 4.03 and below versions" going on to say "this means you won't have PS5 game loading from anything other than demos/freemium." Update #3: Developer @illusion0001 made available some PS5 Game Debug Menus with 60FPS PS5 Game Patches via his Libhijacker Github Fork as well now. Update #4: PS5 4.03 HEN PS4 FPKG Enabler Payload & Porting Offsets by Sleirsgoevy!
