PlayStation boss 'Jim Ryan' has come forward and given us an update regarding backwards compatibility on the next-gen PlayStation 5 console due to hit on November 12th/19th.
It appears that with the PlayStation 4 having over 100 million users, means that efforts to make the PS5 backwards compatible with PS4 games was a target set by the company. They have come forward and stated that 99% of PS4 Physical game will work on the PS5. It is unknown what games won't work with the system but it's my guess that Sony couldn't get round to trying them all and is leaving it with just a small chance that some games may not work, just to cover their own backs.
Now in regards to backward compatibility with PS1. PS2 and PS3, well unfortunately you're out of luck. Sony specifically decided not to try and get the console to play them as they were mainly interested in newer technologies and looking forward at what the PS5 can do. Compatibility with older generations simply could not be achieved with their work fully focused on bringing a next-gen console. Personally I've never really cared for backwards compatibility but I know a group of people are, the good news is that most of your favourite PS4 titles will work