According to a leaked technical document linked to AMD's future desktop CPU Socket AM5, the socket's cooler compatibility with the departing Socket AM4 may stay the same, preventing you from purchasing a new cooler.

It is interesting as two fundamentally different sockets—one a PGA and the other an LGA—have been designed with cooler cross-compatibility (if the reports are correct). The paper discloses that, with a CPU installed, Socket AM5 would line with the retention clip, and mount-hole spacing would be identical to that of Socket AM4 when the processor is installed. 

As a result of the new images, it appears that the socket locking mechanism is largely comparable to those of Intel sockets, such as the LGA1200, and that the socket is not a downscale of TR4/sTRX4, as had been speculated on social media. When the top retention brace is closed, it swings along a hinge and is held in place by pressure from a lever that engages a hook. According to the model, AMD Socket AM5 CPUs have TDP values ranging from 45 to 65 Watts, 95 to 105 Watts, 125 to 170 Watts, and 170 Watts.

This could imply that you can move your pricey liquid-cooling setup or expensive AIO LCS from your previous Ryzen desktop build to your new Ryzen desktop build without incurring additional costs.

AMD Socket AM5 Might Keeo Cooler Mounting Compatibility from AM4