Can't open Nikon D7500 RAW files in Lightroom 5.7, why

Very simple. You cannot update Lightroom with the camera raw plug-in. All of the camera raw technology is part of the Lightroom program, and the only way to get an update is to update the program. Unfortunately, there isn't a free update for Lightroom 5 that will give you direct support for the NEF files from that camera model. You can, however, download the free DNG converter from Adobe and use it to create DNG copies of your NEF files that can be opened with Lightroom 5.7. You cannot use the DNG conversion technology built into the Lightroom that you have because it will only convert to DNG if it already supports the native raw files. Or, you can purchase Lightroom 6, which will support the NEF files from your camera if you apply the updates that have been made available for Lightroom 6. Understand however that Lightroom 6 .14 is the final update for that version and there will be no more updates ever and there will not be another upgrade to the standalone Lightroom. The other alternative would be to subscribe to the Creative Cloud photography plan, $9.99/month in the US, includes the latest Lightroom and Photoshop, and will have the best support for the Nikon D7500.