If they’ve lasted five years before needing a refurb, then they’ve done well. It’s not unusual for white worm to set in when diamond cut alloys are between 2-3 years old.
Some do attempt DIY repairs to remove white worm corrosion - there are various videos on YouTube. I don’t know what the longevity or durability of a DIY refurb would be though or how easy it would be to get a professional looking result, and it’s unlikely you’d be able to replicate the feint concentric circle pattern (a bit like the surface of a CD) you’d get with a factory refurb from the CNC lathe re-cutting the diamond cut face.
If it was me and if I wanted to keep the diamond cut finish (I personally wouldn’t), I’d go for a professional refurb by a good, reputable alloy wheel refurb company. As for the cost; you’re probably looking at around £90 + VAT per wheel. Some companies offer a discount if they’re doing all four wheels.
IMHO the only sure fire way to prevent white worm coming back is to get the wheels refurbished in a painted / powder coated finish which is much more durable than a diamond cut finish. I’ve seen pictures of a mk7 Golf GTD with the diamond cut Nogaro alloys refurbished in a powder coated finish and I thought the looked very good. I’ll try and find the discussion thread an add a link to this post.
Edit; here’s the link I referred to above. There’s a picture of a Tornado Red mk7 GTD in post #12 of the discussion thread with the Nogaro alloys refurbished in a gunmetal / anthracite powder coated finish.
https://www.golfmk7.com/forums/index.php?threads/new-gtd-owner-from-northern-ireland.345425/