For the most part, things are pretty linear. Everything scales up just about the same.
A few points though...
- Weight. Everything weighs more at 10g than 5g. Which often means some of the things you might get away with using gravity start to get unwieldy. For myself and my former brew partner, we had a mishap trying to raise an imperial stout mash to a level where we could use gravity to drain, broke the wooden dowel we were using to hoist it, and spent the rest of the afternoon cleaning his garage floor
-- after that day we went to a single tier system with 2 pumps.
- Time... Heating and cooling will just naturally take longer. This to me isn't a big deal for heating, but when you start trying to cool 10 gallons of wort, you may have to change methods. An immersion chiller won't work as quickly, and probably isn't the best option. Counterflow or plate chillers start to make a LOT more sense. But that introduces things like needing screens/filters perhaps for a plate chiller to keep it from clogging.
- If you're not kegging... You need to start. Bottling 5 gallons of beer is a bit of a nightmare. Well guess what happens when you double it?

For fermenting, I use a 15.5 gallon Sanke keg with
this fermentor kit. Works well for me, and I use the blow-off port to push CO2 for transfer, so I can transfer under pressure. Once the keg goes in my fermentation fridge, it doesn't come out until the beer has been emptied into serving kegs.