This would work. Alternatively, you could do a fully remote install powered by solar/battery with a radio link to the main house. Something like this: https://www.amazon.com/Ubiquiti-UBB-US-UniFi-Building-to-Building-Bridge/dp/B082VJ9GP1/
It's probably going to be easier to get a good connection between the house and garage than from the ISP.
Powerline adapters:
https://www.techadvisor.com/test-centre/network-wifi/best-powerline-adapters-3490638/
Also there is various equipment that can extend the network point-to-point for 'long' distance, especially if there is direct line-of-sight.
For example (I have not used this, but it was at the top of my search):
https://www.amazon.com/Ubiquiti-UBB-US-UniFi-Building-to-Building-Bridge/dp/B082VJ9GP1
That was my suspicion. That I needed to unplug the other end of the cat5 before plugging in the bridge.
I am using the Unifi Building to Building bridge. https://www.amazon.com/Ubiquiti-UBB-US-UniFi-Building-to-Building-Bridge/dp/B082VJ9GP1
I have a cloud key and when you click the BB in the management page it displays the signal strength. I am getting anywhere between 9 and 25 percent. There is a tuning function that allows you to adjust the dish and see if the lights turn blue. But no luck thus far.