I am not aware of any premature (time and mileage) timing belt failures.
What model year is your RX?

The sludge problem starts with extended oil change intervals, which results
in blacker oil, which neglected long enough, will result in sludge.

Unless a pulley or water pump seized up you're probably not going to
see a belt failure before 60K miles or even 120K miles (some owners to
200K miles). But the belt does stretch a bit and it's a good idea to
replace it 5yr/60K miles even if the interval spec'ed more. Some of
these engines are interference and can be damaged if a belt snapped.

It would be a good time to inspect or just simply replace the oil
seals, water pump, valve cover gasket set, PCV valve/grommet and
pulleys at the same time. But you may be able to do that every other
timing belt, depending on the condition of the components.

Sure, blackened thickened oil is the start of the oil sludge problem.
The problem is the higher cylinder head temperature Toyota needed to
pass newer emissions standards. So while traditional sludge starts in
the oil pan, Toyota sludge starts in the cylinder head. You can
inspect the oil passages while the valve cover gasket set is changed.

As a result of the sludge problem in 2004 ALL Toyotas are required to
change oil every 5000 miles instead of the 7500 miles earlier to
maintain warranty.