Let the original number of students be $nn$n. The total age of the class is $15n15n$15n.

The total age of the 5 new boys (average age 12.5 years) is $5\times 12.5=62.55\; \backslash times\; 12.5\; =\; 62.5$5×12.5=62.5.

The new average is $14.514.5$14.5 years. Thus,

$\frac{15n+62.5}{n+5}=14.5\backslash frac\{15n\; +\; 62.5\}\{n\; +\; 5\}\; =\; 14.5$n+515n+62.5​=14.5Solving gives $n=15n\; =\; 15$n=15.

Originally, there were 15 students in the class.