In mafia town when Im about to click on chapter 5 in the first act, it says missing a key item and cannot complete the act or chapter without it.

[KFCBUCKETS9000]

I have no idea what the key item is.

[The Void Boy]

you need the timestop hat

[Dman]

I managed to do it with the scooter badge xP

[Bread]

You need the timestop hat which can be made in act 4 (you will need quite a bit of yarn though).
You can also do it with the scooter.
https://www.youtube.com/watch?v=pgo_kpNLhIs

[Chocice75]

You need to craft the Time-Stop Hat with at least 32 pieces of yarn, with one of those being Time-Stop Yarn from Chapter 4. Then, you can beat Cheating the Race. (Note: The Fast-Hatter badge helps a lot here.)

[Saturn]

You can actually use many tools for this, and may not need to use the Time Stop Hat to complete it.

1. Use the scooter badge, you can find it in Subcon Well
2. When the race starts, run in the other direction until you see a red cannon. Going in there progresses at least halfway through the race
3. Of course, you can always use the Time Stop Hat. You can find it's yarn all over Alpine Skyline
4. And if all else fails, Steam Workshop mods!

[White Altar Prophet]

The item is the Time-Stop Hat, but you actually don't need it to complete the mission. You can enter the mission without having the hat, and there's a simple process to follow. Just buy the Scooter Badge from the Badge Seller, equip the Sprint Hat (which Mustache Girl practically gives you after Barrel Battle), and take as many shortcuts through the course as possible. You might make it. I know I did~