First I showed up to Blackforest expecting to pick up the game from where we left off last week, but a new player showed up and he really liked 5e. Also I had promised Gabe Jr that if it was just me and him I would run 5e if he wanted to play that instead of my OSR madness. Unfortunately for me I showed up completely unprepared for this situation and therefore reran the events of last session out of desperation. (Don't do this. It's bad.)
Second I don't actually have any chase rules that I can call on at a moment's notice. When I knew a chase was about to start I looked up the optional chase rules in Vornheim and cringed when I realized I had no measuring tape with me. (There was none in the shop either.) Luckily I was able to utilize a Star Wars lanyard. I ended up making each side roll a d10 and they would move that many heads across the table. (The lanyard had little heads of Star Wars characters that I was using for vague measuring units.) Whoever made it to the center of the table first won the chase, so to speak.
As cool as lanyard-based chases sound, I don't think it's my thing. But playing cards; those are my thing. So I'm going to layout a playing card based chase ruleset here. Disclaimer: the main inspiration for this ruleset is borrowed from an article, but I found it too wordy to be relied on at a moments notice. So consider this ruleset a wacky simplified version of that one.
Required supplies are simple: a deck of playing cards without the faces and something to represent the chasers and chasees.
Start by laying out d6+4 cards face down. Flip the first card over and place the chasers and chasees on there. The rank of the card is the difficulty class set for each side. (Aces count as 1.) Each round each member rolls a d10+Dex. If the result is higher than the rank then they advance a card. The chasees escape when they reach the last card and the chasers win if they incapacitate the chasees or cut off their means of escape by reaching the end first.
If two members are on the same card they can exchange a round of melee attacks. If there's only 1 card of difference between them then they can exchange a round of ranged attacks instead. Anything more than that and the two sides can't attack each other.
Instead of attacking a member can opt to inflict a disadvantage on an adjacent member (same card or 1 card away) or provide an advantage for themselves. In the case of disadvantage a member rolls 2d10 and takes the lowest and in the case of advantage they take the higher. In order to accomplish either tasks a test of some sort is required, usually a skill check of some sorts but don't be afraid to reward ingenious thought.
If members decide to split up you can place another row parallel to the first and place the figure representing the member doing the splitting on that new row.