A few years ago, my DM ran a chase for our group during a session, following the rules for chases in the DMG verbatim. It was not fun. We spent the better part of half an hour going through the initiative order, grinding through a mountain of chase complications, while a giant Retriever crashed through the brush trying to catch us and we kept asking the DM in our theater of the mind if there was a place to hide from it. A year later, I played Assassin's Creed: Black Flag, my heart pounding as Edward Kenway sprinted down the street, down alleys, and up and down buildings trying to shake off a group of guards of Havana hot in pursuit, and had a blast.
Then, a month ago, I sat in the theater watching Dungeons & Dragons: Honor Among Thieves as Doric the druid led an intense chase, complete with multiple Wild Shapes, several locations at different elevations, arrows whizzing past her, and even a failed Deception check posing as a guard in a stolen suit of armor!
I know that roleplaying games have the capability of providing satisfying and triumphant relief at the end of a worthy battle, so there's just got to be a way to capture that same result during and after a fast-paced, exciting chase scene. Let's look over the current mechanics, where they go wrong, and a possible alternate set of rules to make chases in 5e fun.