Ah, you are using HDMI out.
So the PC isn't actually going to sleep. The monitor is turning off, which shuts down the HDMI port, which stops audio playback. Or maybe you have the PC set to sleep at 5 minutes as well? If so, the monitor is shut down, HDMI is off so playback stops, nothing is playing so PC goes to sleep.
I would have expected the setting you found at Tools --> Options --> Audio --> Settings --> Disable display from turning off (useful for HDMI audio) to take that situation into account. I'm pretty sure when it was created it was so people didn't have to use screensavers instead of shutting down the monitor. Maybe some searching on the forum would find the original discussion.
If the existing functionality doesn't cater to your situation, maybe it could be enhanced to do so. Simple logic: If audio is playing and the output device is HDMI, don't allow the monitor to sleep. That would simply parallel the existing video functionality.