Can't Update iMac past 10.10.5

Hello. A family member has a 2010 iMac that hasn't been updated past OSX Yosemite 10.10.5, and the device needs to a software update in order to make several other updates, including browser updates. The device doesn't provide any software update options in the About My Mac tab and I've searched for solutions. I've researched that I could download El Capitan but it said I needed another version in order to install it. I moved on to try downloading High Sierra but when I attempted to install it I got this error message:

I had downloaded the High Sierra update from an official link. I then attempted to download regular Sierra. But the only official download link I could find was for 10.12.1, and when I attempted to install it I got another error message saying I needed 10.12.0 first. I've looked for solutions on how to update this Mac but I keep getting the same answers of El Capitan and High Sierra. I know this is an old Mac with an old operating system, but I'm hoping to get this figured out.

Thank you for any advice!