GitHub - IH0kN3m/Awesome-PS4-Jailbreak: A list of PS4 Jailbreak links.
Adieu: PS4 Kernel exploit for firmware 4.05 and below, fully detailed by team Fail0verflow - Wololo.net
PS4 Jailbreak: STATUS (OPEN) | PSXHAX - PSXHACKS
According to theflow0 disclosure for BD-JB exploit, here is some table chart which exploit is working and which exploit is not working for each console PS4 and PS5 with their respective firmware :
PS4 Jailbreak Guide - HEN Exploit on 5.05 - CFWaifu