The Rhino 5 trial will load plugins for as long as it allows you to save, which is 25 times. Not sure if that includes Auto-Save, so I might recommend disabling that immediately. By default, MXS files are saved in the same folder as the current 3DM, or else in C:\Users\[username]\Documents\Maxwell\output, if the current 3DM has not yet been saved. You can check whether the MXS is being written, or you could just try to write another -- if the MXS that would be written already exists, the plugin would pop up a window to confirm whether you want to overwrite it. Absence of that confirmation would imply that the MXS is not being written.
From your description of the situation, I can't tell what is happening. You have a toolbar with the plugin's buttons, and you have the Maxwell menu, so you have set Maxwell as current in Render > Current Renderer menu. Those things can't happen if the plugin is not installed.
- Do you see any errors printed in the Rhino command line?
- Do you see a window open if you click Maxwell > Plugin Windows > Log Viewer?
- If so, do you see any errors printed in the Log Viewer window?
- Which version of the plugin are you using?
- If you click Help > About Rhinoceros, what is the Rhino 5 version and build date?
To preempt question 4, I'm guessing you're not using the current plugin, and if so, I'd first use Programs and Features to uninstall any versions of Maxwell for Rhino, then download both the x86 and x64 installers again, and install them both, provided that the OS is 64-bit, and that Rhino 5 has installed both x86 and x64 architectures.
As for your friend not updating their Rhino 4 installation to SR9, you should tell them they are crazy. Because they are either crazy, or pirating and afraid to update. Major issues are addressed in Rhino SRs -- it may not be apparent, since they are both Rhino 4, but Rhino 4 SR0 was released in 2007, and SR9 in 2011. That's an awful lot of development to ignore.