Sounds like it should work ok. Will you have any settings on the TV or PS5 to alter the sound/picture sync?
If not there's always a Hdmi to Optical cable you could buy, but they need to be powered too.
https://www.amazon.co.uk/eSynic-Extractor-Splitter-Optical-Converter/dp/B0CMCRRPBS/ref=mp_s_a_1_7?crid=2FT0QDF6AM5S2&dib=eyJ2IjoiMSJ9.XSUv-NlJfQsfP2j6gkaoYFNMyYbe4HYMf8Pldr5H4KGIi8GQ4Ek72pYUUQzNbW6dIM30ncSlRPKKL3JlqprqOr3FkM6CqIdt_5BElCfaN_ij6yetKiOr9hNpHKiKTX3i3z92GsZqSgaLGLBM1ZfMpJbq4riIwjufPO_naNPFwcDhs6j4cutoDRNIACS6vbuLyRRJOpV6Nz7vD16yoaaKMw.9k-GUARjsOTuanNNhV-fkdi8ZHv2_3MUDMqp_dXelk8&dib_tag=se&keywords=hdmi+to+optical+cable&qid=1714138537&sprefix=Hdmi+to+optical%2Caps%2C135&sr=8-7