For the push button example I can envision using a pair of 555s or a 556 as a timer for the flashing and a latch to store the success condition, but how does it

For the push button example I can envision using a pair of 555s or a 556 as a timer for the flashing and a latch to store the success condition, but how does it count to 5? You need more logic in here, so why not a cheap programmable chip?