Here is a really dumb solution to 2.
By the Chicken McNugget theorem (yes, it has a name, look it up on AoPS), the largest number of pencils that cannot be bought is 5*12 - 5 - 12 = 43.
Since 43 - 5 - 5 = 33, it is impossible to buy 33 pencils, because if there was a way to buy 33 pencils, then we could also buy 43 pencils by adding two more 5-packs, a contradiction.