Digital clocks show hours and minutes, such as 14:37.

How many minutes per day does at least one five light up on these clocks?
A 5 cannot light up in the first position. We will first consider the interval of the first 12 hours:

- A 5 lights up in the second position for 60 minutes (from 5:00 to 5:59); for the other positions, we therefore consider only the remaining 11 hours.
- A 5 lights up in the third position every hour for 10 minutes (from **:50 to **:59); in total, $11 \cdot 10=110$ minutes.
- A 5 lights up in the fourth position six times every hour for 1 minute each $(05,15,25,35,45,55)$, but we count only 5 minutes, as the minute $* *: 55$ is already counted in the previous paragraph; in total $11 \cdot 5 \cdot 1=55$ minutes.

At least one 5 lights up in the interval of 12 hours $60+110+55=225$ minutes, so for the entire day it is $2 \cdot 225=450$ minutes, which is 7 hours and 30 minutes (a 5 also lights up in the second position from 15:00 to $15: 59$).

Another solution. From 5:00 to 5:59, a 5 lights up for 60 minutes in the second position (the same from 15:00 to 15:59). For each of the other 22 hours, we can list the minutes in which at least one 5 will light up: $05,15,25,35,45,50,51,52,53,54,55,56,57,58,59$, which is a total of 15 minutes. Altogether for the entire day, it is $2 \cdot 60+22 \cdot 15=120+330=450$ minutes.