I have a 05 ford focus that when I turn the headlights on the radio mutes. Turn the lights off radio back on. Checked fuses. Could it be the battery saving relay by chance.

Thanks

Remove and fully charge, or replace, the battery and test the alternator:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-10.html#post1973613