H.264 and H.265 standards carry profiles, which represent a standard of support. So it remains possible (maybe) your TV can play H.265, but perhaps the videos you tried were encoded with a profile that exceeded what it supports.
For H.265, the most basic and widely supported profile is called “Main”. The standard carries many more higher level profiles, most of them using “Main” with something tacked on, like “Main 10” or “Main 4:2:2”. For testing purposes, avoid those.
In Handbrake, you might try encoding x265 to the Main profile, and perhaps no larger than 1920x1080 (in case it’s bigger) and see if that plays. Stick with common AAC or MP3 audio in a MOV or MP4 container. If it still doesn’t work, then I’d essentially say that confirms it doesn’t support H.265.