In reply to The Ex-Engineer:
> > Unclimbed 6000m peaks have been a bit of a rarity for decades
Er, no. There's dozens and dozens of *decent* unclimbed 6000ers left and hundreds left, if you count every snowy mound as well.
5000m doesn't mean much in the Himalaya-Karakoram-Pamir or even the Andes. There are many passes that high and almost countless peaks and points.
There are only 12 or 13 independent unclimbed 7000ers left, if you count peaks with at least 6% prominence - the highest being the untouchable Gangkar Punzum (7570m). There are a few more less prominent summits in this range, some even named, like Muchu Chish and Summa Ri, that would be decent climbs but don't poke up above their massif much. One of the remaining independent unclimbed 7000ers was climbed this year - Gasherbrum V (7147m), by a Korean team.
Once you get down past 6800m there's more than enough unclimbed peaks to go around, some of them really impressive. Nearly all of them never get touched or even looked at.