My favorite 5e house rule is my favorite house rule for any D&D or D&D-Adjacent RPG, it's the worlds most common house rule, and it's not even a rule so much as ignoring a rule that's ponderous, annoying, and makes the game less fun.
I call it "En-what-brance?" and it's where you don't track the weight you're carrying. At all. Eff that noise. Oh you're wearing plate, carrying a coil of rope, and your strength is only 16? Congratulation your speed is 5' and you take a -7 to all actions! FUN! [Note: don't quote correct rules at me it's called hyperbole and you need to learn rhetoric]
Also closely related is "I'll track ammo when hell freezes over and I will come across the table at you if you mention it again Greg so help me."