My wild arsed guess is one of your human interface devices has a macro triggered by "mouse button 5" and mimicking "mouse button 5" , causing it to double up or you got an VID/PID conflict.
if you got any other compliant mouse with 5 buttons (i.e. can work without custom drivers), plug it in and check to see if same problem occurs.
Next step would be to plug your RAT into another PC, do not insall drivers, , see if it's a physical problem with the physical key switch.
Then install the drives on other PC, see if it IS the drivers.
IF not physical, and not the drivers, then plug RAT back into gaming PC, turn on handicap accessibilty onscreen keyboard, and disconnect the Saitek keyboard and turn off password login, and reboot.
After that, well, drive sweeper or something similar to completely delete the RAT drivers and start over? IDK, it's not easy, this could be an old school HID IRQ or DMA conflict.
!!! Real tech support questions no one under 30 in the PR community knows about. !!! We're getting old. I haven't had a similar problem since a game controller port issue in MS Flight Sim on Win98
Sound like VID/PID (Vendor/ Product ID) conflict.
keyboard and or peripheral and or and the mouse share the same VID/PID.
USBDeview is a good tool to check and recover this problem.
Plug off the keyboard, and run USBDeview.
Find the VID/PID of the keyboard.
Is the VID/PID assigned to the mouse, too?
If so, Right-Click and "Uninstall" both of them.
When the mouse is plugged in again, Windows will automatically install it.
You have to change the VID/PID of the keyboard or mouse.
On the firmware, VID/PID is defined in the device descriptor.
On the host app, VID/PID is also used to find the device. This could get tricky in web browsers... I's a whole other thing to get sorted in the about:config or maybe requires a registry tweak.
USBDeview
View any installed/connected USB device on your system
Another option,...
Download PortableApps,
PortableApps.com - Portable software for USB, portable and cloud drives
install to hard drive or thumb drive,
download FF or Opera portableapps versions.
Mozilla Firefox, Portable Edition | PortableApps.com - Portable software for USB, portable and cloud drives
Opera, Portable Edition | PortableApps.com - Portable software for USB, portable and cloud drives
Test to see if same problem occurs in those browsers.