The computer school enrolment shows that there are 5 girls in every 12 boys. If the school enrolment in one year is 5,200, how many girls and boys are there?

ratio of girls : boys = 5:12 = 5x : 12x

5x + 12x = 5200
17x = 5200
x = 305.88...
should have been a whole number.

You said: " there are 5 girls in every 12 boys"
I read that as : there are 5 girls for every 12 boys

It should have said "approximately 5 girls for every 12 boys"

You decide what the problem is with your question