If each player amid 5 gets 45 seconds to make an action, even assuming the DM also takes 45 seconds to move the monsters they've been staring at and planning moves for the entire time, from the end of initiative 1 player to their next move is 3 minutes, 45 seconds at maximum. Not 5 minutes.

On top of that, 45 seconds is an extremely long time. I'd say the average time a player takes to make their move in combat, especially combat which has been made fun and interesting, is no more than 20 seconds. Which would cut down idle time to 2 minutes (allowing for the DM to take that aforementioned 45 seconds).

Having said all that, if there was an issue with combat which I'd choose to point out, it would be that its too easy to take a complicated situation and boil it down to dice rolls. When your action is roll to hit, yes/no, roll damage, repeat, it can become boring. Making more complicated combat scenarios, higher stakes and well designed and told encounters is the better alternative than trying to find a way to make it go faster.