Does cooking reset the expiry date of ingredients?
The expiring date of the cooked food has nothing to do with the expiring date of the ingredients. They are considered separately. A cooked food has a shelf life of 3-5 days, and this assumes that you followed a safe cooking process, which includes using ingredients which were not expired at the time of cooking. 

Cooking does not sterilize food, but it reduces the bacteria currently alive in it. It doesn't kill them all, and it doesn't remove toxins, so it is not a "reset" and you cannot make unsafe food safe by cooking it. But the expiry date is calculated with such a margin that the bacteria which are left after cooking cannot get to dangerous levels too fast, so you still have the regular 3-5 days. 

On the other hand, if you have two different ingredients with a long expiry date and cook them together, the new expiry date is not determined by the date of the ingredients, not even by the date of the shortest lived ingredient. It is still 3-5 days.