1. Some encounters in published adventures are may be written assuming six seconds per round.
This is probably the most significant problem. I can give a couple examples. From Storm King's Thunder, there is an encounter involving timed hazards:
Characters who have a passive Wisdom (Perception) score of 14 or higher notice gaps in the ceiling, suggesting the presence of two hanging blocks of stone. Characters who search for traps and succeed on a DC 14 Wisdom (Perception) check also notice these blocks, which constitute the temple’s outer defenses.
Each block is a 40-foot-tall, 40-foot-wide, 20-foot-thick slab held up by mechanisms buried in the mountainside. When the lever in area 2A is moved to the down position, the block of stone closer to the entrance (area 1) falls, sealing off the tunnel. When the lever in area 2B is moved to the down position, the inner block does the same thing. Each block takes about 6 seconds to drop to the floor, allowing time for creatures to get out of the way.
At 6 seconds per round, the party has a single turn each to get out of the way of the hazard. At 5 seconds per round, they potentially have two rounds (how are you going to adjudicate 1/5th of a round?).
We see a similar issue with an encounter in Tomb of Annihilation:
With a successful DC 15 Wisdom (Perception) check, a character discerns that the entire floor of the corridor is a single pressure plate. The adamantine propeller has AC 20, 30 hit points, and immunity to all damage except force damage. It thunders into motion whenever more than 20 pounds of pressure is placed on the corridor floor. Once activated, the propeller spins up to full speed in 6 seconds. If the weight is removed from the floor, the blades take a full minute to slow to a stop.
While the propeller is spinning up or slowing down, a creature can leap through a gap between two blades with a successful DC 20 Dexterity (Acrobatics) check. On a failed check, the character takes 33 (6d10) slashing damage as it passes through the blades.
Again, a timed hazard, where a 5 second turn potentially gives the party more time to avoid it.
2. It makes the Acquisitions Incorporated spell gift of gab a bit odd to rule:
When you cast this spell, you skillfully reshape the memories of listeners in your immediate area, so that each creature of your choice within 5 feet of you forgets everything you said within the last 6 seconds.
When used in combat, casting the spell would retcon anything you said on your last turn. If a turn is five seconds, now it can include words from the last two turns.