Upgrading to 10.10 ether via USB drive or app store, in September 2016 I've got a mac mini running 10.8.5 that I want to upgrade to a newer OS. The most recent OS I can upgrade to is Yosemite 10.10.5 (due to the fact some software we need to run doesn't work on 10.11 or the upcoming 10.12).

I've got the installer for Yosemite 10.10 saved to a USB flash drive from when I did a previous clean install. Am I able to use this on my 10.8.5 machine if I want to do a standard upgrade not a clean install? 

If not am I still able to upgrade to 10.10 via the App Store?
App Store 

You can easily check whether upgrading via the Mac App Store is an option by going into the App Store app and seeing if it's available for you. 

Generally, what should happen is the App Store will give you the option of upgrading to the most recent OS that'll run on your Mac Mini. Your question doesn't specify which model of Mac Mini you're running, but any Mac Mini from early 2009 onwards can run macOS Sierra, so you're likely to get the option of upgrading to that, which you don't want. 

You may be able to still use the App Store by going to the Purchased tab and seeing if Yosemite is listed (it will be if you've previously downloaded it using the same Apple ID).

USB Drive 

Regarding your USB option, this may work depending on what version of the installer you have or how you put the installer onto the USB drive (e.g. Is it bootable from the USB)?

Assuming everything has been done right, then Yosemite supports the usual installation options, including "upgrade install".

Remember: 

The best approach (as always) is to do a full backup prior to attempting the upgrade, regardless of how you plan to do it.