Not sure what you mean by “no receiver”, is that an AVRreceiver? The Sonos PLAYBAR doesn’t need on, it works with an optical connection to the TV, and interprets the Dilby Digital signal inside of it.
A Sonos sub could easily be added to the PLAYBAR, again with no need for a receiver.
The issue comes when you want to use existing speakers for the surrounds. This requires use of a CONNECT: AMP, which has to be connected via an Ethernet cable to the PLAYBAR ( or your router, and the PLAYBAR needs to be connected via cable as well)
Here’s an FAQ on this site that explains how to set up a CONNECT:AMP as a surround driver.
That set up would give you the 5.1 you’re looking for. I’d honestly be tempted by ditching the existing speaker and getting a pair of Sonos Ones to use as surrounds instead, but that’s just an opinion.
Bruce