PlayStation 5 will not be backward compatible with ps1,ps2, and ps3 but will come with 99% backward compatibility with ps4. In a recent interview Jim Ryan (president, and CEO of Sony Interactive Entertainment ) stated that "So unfortunate, we couldn't achieve compatibility with those formats".
       
        When asked about the possible inclusion of the older ps titles Ryan replied "We keep in mind the engineering specialized for the ps5, as we produced the device. In the midst of that, the PS4 already has 100 million players; we thought they ought to want to play PS4 titles on the PS5 as well indeed, so we included compatibility with the PS4. While implementing that, we also focused our efforts on taking in the high-speed SSD and the new controller DualSense at the same time."

But recently it is being rumored of possible ps1,ps2, and ps3 emulation on ps5 via the cloud but we can only say for sure once and when there is any official news or the launch of ps5 itself. But you can play some of the biggest titles like Uncharted, God Of War (series), Last of Us Remastered, and Bloodborne of PlayStation via ps now.

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