The D500 is an action camera and the D7500 is an all purpose camera. Both cameras are excellent - but in a nutshell that's the decision.
The D500 frame rate and large buffer are tuned to photographing action. The AF system is new and excellent producing a big improvement in the keeper rate. For action, there is a big difference. The fast memory cards further support the idea of an action camera. The camera has the latest technology but carries a premium price. There is a bit of a learning curve with the D500 - for example the AF system is new and old settings and technique will need to be updated.
The D7500 is a very good all purpose camera. It replaces the D7200 with some modest upgrades. It has an on-camera flash which may not be the best option, but provides a very good option for casual images. The frame rate, buffer, and memory cards are all good, but reflect the use of older technology. Compared to most cameras you will be perfectly happy - unless you are photographing fast action. It's not that the D7500 is unable to photograph action - it's similar to earlier cameras. It's just the D500 is outstanding.
I bought a D500 for my own use, and a D7200 for my wife more than a year ago. Buying today, she'd get D7500 rather than a D500 as her photography is more generalist in nature. Sure - she photographs foxhunting and birds in flight - and the D7200 is fine for those. But for regular use with those subjects, the D500 is a nice step up.
Both of these cameras are excellent. They both are solid and have a typical Nikon layout of controls. If you are used to earlier models, you'll have little trouble picking up either of these cameras and shooting it immediately.