Typically, a low toner cartridge doesn't lead to dirty prints (I assume
you mean the white areas have a gray cast on them), unless you have had
to crank the darkness way up to get a darker print).
I don't know how the Brother printers are designed. However, if there
are any accessible corona wires (these are a thin silver wire strung
across the width of the printer often part of the drum unit, looking
like a steel high E guitar wire) and make sure they are not coated in
toner. Often the company provides a little cleaner device (usually made
of felt) to clean the wire. This needs to be done with care, as the
wire is stretched tightly. Also, check for any window that transmits
the laser light to the drum and make sure they are clean (use a soft
brush to remove any residual toner that may be obscuring the light).
You are correct that the drum should last a few toner cartridges, in
general, but the drum life is really based upon the amount of light
exposure it gets, so if you do a lot of printing with very low toner
coverage (like text and toner saving) the drum may get much more use
than the average toner cartridge yield would imply.
You mention the page count was over 5000, so the question is what is the
rating for the drum?
Also, if you have exposed the drum to very bright light (like direct
sunlight) that can damage the surface of the drum and limit its life.
Lastly, if you are "handy" you may be able to buy a replacement drum and
install it into the drum unit. The drums can be purchased from some
rebuilder/refurbisher suppliers, and some are only about $10. They
often come without the gearing that is needed on the ends of the unit to
interface it with the rest of the printer, so you have to figure out how
to remove and install them on the new drum without damaging things. I've
done this successfully with a Panasonic unit which used the exact same
drum as the HP II cartridge unit. However, I don't know which one the
Brother requires.
If you don't want to get "into" the machine, before investing in a drum
unit, it may be worthwhile having someone in service look at the unit,
as it may just need a good cleaning.
Art