The mirror lock up option in 'Maintainence'/'Set up' for my FujiS5 Pro is grayed out so I cannot use it. My sensor is dirty and needs cleaning.

You can't take photos when mirror is in lock up mode. That is used to clean the sensor(dangerous to do if not properly equipped!). Turn off power to camera to snap mirror back up and then you can switch to manual mode to shoot long exposures. Hope this helps!!

Check the batteries

this can be an issue with the following check the comb electrode this is also know as the charge grid is it dirty damaged clean this unit replace comb electrode if damaged is the cleaning blade dirty is the drum being cleaned correctly by the cleaning blade is the drum past its life replace are the mirrors dirty clean them
the above will resolve your issue

Are you talking about spots you see on the pictures? Are these spots you see in the same place on all the pictures? If you really want to see if your sensor is dirty pick a clear day with a great blue sky focus to infinity and then shift the lens to manual focus and the program to "P" take a pitch of the blue sky. Then down load this picture to the computer and open it up to 100% and look it over if there are spots then the sensor should be cleaned. Even if you take the lens off and look into the camera body you still can't see the sensor all you are looking at is the mirror inside the prism box.
To clean the sensor you need to put the camera into "clean" mode which locks the mirror up. It may be possible you just have a dirty lens or UV filter.

Normally, you can manually lock-up the mirror for the purpose of cleaning the sensor. To do this, you need to connect the camera to the optional EH-6 AC adapter. If after removing the lens and inspecting the mirror, you cannot gently nudge it back down (do not touch it...use a cotton swab) then you'll need access to the EH-6. If you don't have one, possibly a camera store near you would have one and be willing to let you plug in your camera so you could try to access the mirror lock-up function in the set-up menu.

Call Canon at their website for information. Go to Canon.com/ support/ repairs Then find the toll-free phone number.

above the imaging unit should be a recess with a clear window (1/2" X 12") that is your laser window which writes to the drum, make sure window is clean, if that does not help you have a dirty Polygonal mirror (six sided mirror that spins) inside your machine and it needs to be cleaned or replaced by a technician

You should be able to set the exposure to "B" when the exposure is set for manual exposure settings. The shutter should stay open (and the mirror up) for as long as you keep the shutter button pressed.

Mitsubishi mounts the remote sensor on a small board that utilizes the mirror. Most of the time I would suggest that the batteries be checked, as that is what I find the problem to be in most cases. You may have already done this, if so you may have a dirty mirror in the set or you may have a weak IR receiver. In either case I could only recommend a technician to disassemble the set and clean the mirror. As a technician, the mirror is the hardest surface to clean, because the silver is on the front of the glass.

I hope this information allows you to resolve this issue.
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take the lens out and blow air inside the camera and on the inside part of the lens.