There are numerous reasons why this is clearly not a mint error, but rather as a result from two coins being squished together.
- The font for the "second date" is different - it wasn't a 2018
Lincoln Shield cent that put that there, it was from a 2018 nickel.
- The actual date of the second date, as you've already pointed out, is 5 years after the first.
- The second date is written mirror-incuse, not raised. That means that whatever did the pressing of the second date was a coin, and not a die.
You would need an extraordinarily improbable chain of events to create such an error in the Mint - you'd need to make a perfectly normal cent in 2013, have it float around in the mint undetected for five years somehow, then somehow land in the coin press while it was striking nickels in 2018, and to have the ejector in the nickel press fail so that it isn't ejected, land in such a way that it get squeezed by an actual nickel, rather than by the nickel die, and to have the press then running at such low power that the whole thing doesn't become a mangled mess.
Making such a coin outside of the Mint, on the other hand, is extraordinarily easy: take a normal 2013 cent, and a normal 2018 nickel, and put them in a vise, or some similar tool capable of squeezing two coins together. Or even maybe just put the two coins, stacked on top of each other, underneath a piece of wobbly furniture and leave them there for a couple of years. Plated zinc is softer than cupronickel, so the zinc cent will take damage first.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis