It sure sounds, no pun intended, like you have network issues internally. That connection speed you mention is likely between your router and the outside world, and as such would have little to do with the speed inside your network. 

I suspect that purchasing the “professional mesh system” did little to resolve your issues, in fact there are many threads about how much difficulty they add to a hopefully simple network.

There’s several things I’d recommend, in the face of a lack of information about your system, and your network.

First, I’d try a simple network refresh, by unplugging all Sonos devices from power, and while they’re powered down, reboot the router (or all of them? Not sure why three separate routers are necessary, Sonos works from a single subnet, not multiple subnets. Unless you mean extenders, rather than routers, which is different, and Sonos does say that they don’t work with extenders frequently, due to the fact that they often split systems into multiple subnets….but as you have one device wired, that’s a moot issue). Once the router(s) have rebooted and stabilized, plug the Sonos devices back in to power. 

Make sure your PLAY:5 is plugged in to the “main” or “Base” or “root” router, and not one of those others you mention. 

Double check the information in the wifi interference FAQ, especially around competing wifi signals, either from inside your network, from devices too close to others, or from external influences, such as neighbors, etc. A “few feet” is generally accepted to be three feet, for Sonos’ purposes, but older devices are less capable than newer ones in rejecting interference, so be cautious. 

Finally, I’d recommend that you submit a system diagnostic within 10 minutes of experiencing this problem, and call Sonos Support to discuss it. Having hard data to look at would go a long way in helping identify what the issue is, and unfortunately, the vast majority of us on this community forum don’t have access to your diagnostics. 

There may be information included in the diagnostic that will help Sonos pinpoint the issue and help you find a solution.

When you speak directly to the phone folks, they have tools at their disposal that will allow them to give you advice specific to your Sonos system and network.

Having suggested to @mike11292 that he should start a new thread with this topic, I continued posting on the other thread. Probably best now to continue over there.  My fault.