I think if you use a garmin (topo) map, which supports the active routing, you will get more special mountaineering routes, if yoy calculate the route on the 5x. The avoiding settings of the mountaineering app for routing have one more avoidance to choose: climbing paths.
I use the 5x in combination with the garmin topo pro Germany v 7. On the German garmin homepage there is an explanation of active routing ( I didn't find it on the garmin.com page).
https://www.garmin.com/de/topo/activerouting/