If the hands had been fouling, it would not have run for the past 20 years. Do you wind the clock regularly? I do most of my 8 day clocks between 10 &11 am of a Sunday. I think that if you value this clock, you should find a repairer. Does the clock bear any makers name or other identification? TNP has recommended washing the escapement bearing with alcohol. That will remove the crud from that bearing. What about the other moving and rotating parts? Cleaning methods & lubricants for clocks have moved on tremendously in the last 10 years.
Hmmm. If it had usually stopped at around 5 to _any_ hour, I'd have said that it could just be the extra resistance it encounters as it raises a couple of levers prior to striking. A check for this would be, if it's stopped at 5 to (+/- a couple of minutes), to advance the minute hand very gently. If it feels stuck, and has to be reversed before it will go forwards, the fault is in the strike mechanism: if, as soon as you move it you hear a short "whirr", and perhaps a click, it's possible that general wear, tear, and dirt are absorbing so much power that the effort of lifting the levers is the last straw that stops it.
If either the strike wasn't working, or had been allowed to run down, the resistance encountered could, depending on the exact design, be much greater at one particular hour. (If it was an unsprung rack tail catching on the snail cam, if anyone's bothered)
Sounds like it could be due for a clean and oil, but it may also be sensible to do some rebushing and even spring replacement while it's in bits. Which will probably cost more than the clock is worth.
If you're tempted to d-i-y, please read the warnings I gave in February in the thread "Cleaning Clock Mechanisms".
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