You are essentially asking if you can use a USB 2.0 extender cable in your setup. The answer is "it depends".
First, formally the USB specifications disallow cable extenders, for the reason that every extra cable imperfection (two extra connectors and two cable fan-outs at solder joints inside cable molds) usually degrade the high-speed signals beyond acceptable. Quality of extenders, however, vary greatly, so your mileage can vary.
Then, it depends whether you/your users/customers are going to plug USB devices with extra long 5-m cables. Then your extra extender will likely kill the USB functionality in high-speed mode. You will have flaky behavior, with unpleasant experience, data corruption, etc. Contrary to the belief in USB data recovery mechanism, it works only in a narrow region of degraded signals. If the channel gets degraded a bit deeper (due contact wear, contamination, different mechanical tension), the channel will just drop off, reconnect back, and cause a lot of troubles.
However, if you plan to use only LS/FS USB devices (mice/keyboards/sound) the extender will be fine.
The hopes that USB port will fall-back into FS mode are also unfounded. The reason is that the FS-HS negotiations are coming at a relatively low signal speed (~20kHz) where the signal degradation is negligible, so the initial connection will be always negotiated as "HS mode", and the link will always start in HS at 480 Mbps. Then the channel will see massive transfer errors, and host will try to recover the port by resetting/re-enumerating it, and process will fall into the same loop.