[GIS] Keeping only POIs X kms from a trace?

[Heck Lennon]

Hello

Archie's Campings* offers a pretty thorough list of campsites in Europe.

Problem is, files are only country-size, so the number of waypoints is overwhelming (Here's the UK for instance**).

To plan bike tours, I'd like to…
1) import a trace from a GPX file,
2) import Archie's list for a given country,
3) filter that list to only keep campsites that are 5 kms from the route, and 
4) export the output to a GPX file.

Since a "gpxpy" Python module is available, I assume this can be done just with a script instead of an expert application like QGIS… but I know nothing about GIS.

Can the above be done with a Python script?

Thank you.

* http://www.archiescampings.eu/
** https://s7.postimg.org/4mck58dbf/Archie.s.Campings.UK.png