I never set time limits per se at that age. It was more a matter of if homework was done, the rooms were clean, etc. And if it was daylight, and the wasn't raining, they needed outside time each day. So if all those things were met, or would be before the day was out, then I had no problem letting them watch/play. However, if they became insolent or rude, then it was turned off and the next day (without addressing it verbally as to why) they either didn't watch/play or it was much more limited for that day.
I did notice a pattern of, the more screen time, the more sharp their tone was and the more they didn't want to be "interrupted" for things like dinner and baths. The more irritable they were in general, with each other as well.
I know families who just made it a rule that there was NO TV during the school week. Only weekends. Then there never was a debate or problem with how much or "it's time to turn it off" issues. It didn't happen M-Th.
Later, when grades became a bigger issue for one of my kids (late elementary) he had to earn screen time. He could use it however he wanted (movies, TV, video games) with the same sorts of rules (homework had to be complete first, etc), but he earned the time. Every grade he made counted towards time. Each "C" was neutral. Each "B" earned 15 minutes. Each "A" earned 30 minutes. Each "D" deducted 15 minutes. Each "F" deducted 30 minutes. or something like that... I don't remember exactly. But in elementary grades, they got a LOT of grades each week compared to middle and high school. Sometimes 8-10 grades. So he *could* earn up to 6 hours each week (or more, depending). Or not, if he didn't apply himself and work hard. And he was allowed to bank time, so if he wanted to watch a movie, but only got 5 grades that week and only earned an hour of time, he could add it to a running total until he had enough time to watch a movie, if that is how he wanted to use the time. We counted all movies as 2 hours (unless it was less than that in actuality).
This system worked pretty well. He restricted himself from using too much mindlessly, b/c he wanted to play video games on the weekend or with friends, or watch a movie. So he didn't waste it without thinking about it.
It can become a chore to keep up with, depending upon how communication is handled with the school, but if you are up for it, I found it to be an excellent solution to screen time. (and an encouragement for better grades). BUT, you have to know your child and what they are capable of before you set up the scale/rules. You want the rules to allow them to achieve what you are ok with them achieving, and yet not make them feel like failures for not ever being able to get what they want out of the system. Don't set them up to fail. Set them up to be rewarded for quality work effort. :)