That's not the only way to play PS4 titles on PS5. And on both the standard PS5 and PS5 Digital Edition, you can download your digital PS4 games to the new console. This means that if you have the standard PS5 model with a disc drive, you can insert your PS4 discs to play those titles.
If you didn't know, the PlayStation 5 is backward-compatible with nearly all PS4 titles. The only exception is if you use Remote Play to control your PS5 from another supported device. You cannot play PS5 titles with a PS4 controller. However, you can only use PS4 controllers to play PS4 games.
Yes, the PlayStation 5 supports PlayStation 4 controllers (DualShock 4 is the official controller name).
Can You Use the PS4 Controller on a PlayStation 5?