How do I connect a surround sound system on Apple TV HD gen 5 now that they removed the audio output?

If your audio system has HDMI-in and HDMI-out (video passthrough), then you can connect as

Apple TV →[HDMI]→ AV receiver →[HDMI ARC]→ TV

If you TV supports audio passthrough, then you can connect as

Apple TV →[HDMI]→ TV →[HDMI ARC]→ audio system

or

Apple TV →[HDMI]→ TV →[optical/coax]→ audio system

If the above are inconvenient for your setup, then you can consider an ‘HDMI Audio Extractor’.

Apple TV →[HDMI]→ HDMI Audio Extractor →[HDMI]→ TV

↘︎[optical/coax/RCA]→ audio system