No, PS5 does not require a 4K TV. Supported resolutions are 720p, 1080i, 1080p, and 2160p. PS5 can output resolutions up to 2160p (4K UHD) when connected to a 4K display.
PS5 is compatible with 8K displays at launch, and after a future system software update will be able to output resolutions up to 8K when content is available, with supported software.