The be quiet Pure Rock 2 (155 mm) is generally compatible with your AMD Ryzen 7 5800X, as it supports the AM4 socket. However, it may not be sufficient for very demanding workloads, as the processor has a TDP of 125W and the cooler is designed for up to 150W. It may be necessary to adjust the fan speed to achieve optimum performance and noise levels.

For the thermal paste, you can use an inexpensive option such as the Arctic MX-4 or the Noctua NT-H1. These are known for their good performance and are attractively priced.