Explanation:

The average weight of some students in a class = 58.4 kg
Let the total number of students be n.
Total weight of n students = 58.4n kg
The average weight of 5 students = 62.8 kg
Total weight of 5 students = 62.8 $$\times 5$$ = 314 kg
The average weight of (n + 5) students = 58.4 + 0.55 = 58.95 kg
Total weight of (n + 5) students = 58.95(n + 5) kg
Total weight of n students + Total weight of 5 students = 58.95(n + 5)
58.4n + 314 = 58.95(n + 5)
58.4n + 314 = 58.95n + 294.75
0.55n = 19.25
n = 1925/55 = 35
$$\therefore$$ 35 students were initially in the class.