Oof, regarding "Smart" TVs, five years old is a lot. They are like smart phones in that regard, and often software support stops after a couple of years. Thats likely why the speedtest did not work, the browser may simply be outdated. Please make sure that the Netflix app is still properly supported on your TV.
There are other speedtests available. Especially since you want to use Netflix, you should try fast.com, that is actually owned by Netflix and uses their infrastructure.
Otherwise, an indicator might be the raw wifi connection speed, if the TV is on wifi. That should be visible in the router if the TV itself does not show that. Take roughly half of that as a ballpark.
If the TV is on ethernet i would not expect any issues.