Why was silver given to Aharon and his sons in Numbers 3?

Answer From The Annual Reading Schedule - Week 32 Notes For Numbers: When Yahweh struck the first-born sons in Mitsrayim (Egypt) and spared the first-born sons of all the Yisra'elites (Israelites), He set apart to Himself all the first-born sons in Yisra'el (Israel) (Numbers 3:13). In other words, because Yahweh saved the first-born sons of Yisra'el by the blood of the Passover sacrifice, they became His to serve how He chose. However, instead of taking the first-born sons of every single tribe, He took the entire tribe of Lewi (Levi). So the Lewites (Levites) were the "ransom" for the first-born in Yisra'el. A ransom is something that is given to release something else or free something else, usually from a state of imprisonment or confiscation that is negative. In this case, the Lewites were given to free up the first-born in Yisra'el from a required duty.

However, there were more first-born in Yisra'el than there were Lewites. So in order to account for the greater number of first-born in Yisra'el, five sheqels of silver were given for each additional person more than the number of Lewites. The math is as follows: