How can I check for radar on 5 GHz DFS channels?

If you were just looking for interference in general, not specifically radar signals triggering DFS channel switches, a 5GHz spectrum analyzer, such as a MetaGeek Wi-Spy DBx, would do. However, a spectrum analyzer mostly just graphs how much energy it sees on various frequencies over time, without actually being able to differentiate between Wi-Fi, radar, and other things that use 5GHz. So it wouldn't give you any insight into whether radar-triggered DFS channel switch events are happening.

If you specifically want to see if your equipment is detecting radar on DFS channels and switching channels because of it, you should enable verbose logging on the Wi-Fi subsystems/drivers of your APs and client devices, and watch for radar/DFS/channel-switch events in the logs (the details on how to do this can vary wildly between platforms and Wi-Fi chipsets, and is beyond the scope of this question).

Another thing you could do is log what channel you see your AP on, and see if you ever see it change channels. Make sure you're checking what channel it's actually using, not what channel you asked it to try to use.

To check for non-WiFi signals, you generally can't use the built-in hardware. The hardware that's built into your devices only does WiFi and it can't detect any other signals. Some provide some "interference" metric, but that's it.

To properly check, you need some sort of generic receiver, preferably a spectrum analyzer. A relatively cheap option is an RTL-SDR USB dongle HackRF, with a 5GHz antenna. This will allow you to observe the spectrum around the 5GHz WiFi channels.

Radar should show up as a wide strong signal:

Another option is to contact your local HAM radio club or a local HAM operator. They will most definitely have the equipment to look for local interference and are more than likely to be willing to help you out.