Mixing Ethernet Cables

Hello All,

I have a question about mixing ethernet cables of different ratings.  My house was wired 20 years ago with Cat 5 cable.  My listening room is in the basement which is two floors away from the router.  Wifi to my streamer has been OK but occasionally drops out so I would like to connect my streamer via ethernet.  Running a new cable (Cat 6a or Cat 8) from the router to the streamer would be very expensive (labor cost).  I can split existing Cat 5 in the basement with a switch and run a patch cord from the switch to the streamer.

Would running Cat 8 from the switch to the streamer be of any benefit given that the signal is only Cat 5 from the router to the switch?

Thanks.