Are you sure its not firing? Have you checked for spark by holding a spark plug against the engine to see if its sparking correctly? A timing light could also check for spark pulses.
It could be cross firing. 1 and 5 are next to each other in the distributer cap. Tha cap may be cracked and have carbon tracking between the two. Cracks can be hard to see. That could cause 1 and 5 to fire at the same time and when you do your test its giving confusing results.
If you have a multi meter, you may be able to detect carbon tracking by removing the HT leads from the cap and measuring the resistance between all the poles. See if 1 to 5 is different from the others. Note the position of the leads before you remove them. Its easy to switch them and mess the firing order up.
If it looks old, investing in a new distributor cap at this point probably be a good move, wouldn't hurt.
Chas
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