If I remember correctly, 3 long, 2 short is most likely a RAM issue for most HP models. In fact, blink codes in general are most often cleared on laptops by a simple reseat of your RAM.
That seems to coincide with your “every now and then” sort of experience. Maybe one of the sticks is just loose.
If you confirm the exact model number of the machine, we can probably confirm this and get some service documentation. But I would pop off the bottom off the laptop, unplug the battery (the regular one, not the CMOS one), then pull your RAM stick(s) out, then put them back in and see if you’re in business.