We have, 99 = 100 - 1
∴ (99)5 = (100−1)5 = [100+(−1)]5
=

5

‌

C0(100)5+

5

‌

C1(100)4(−1) +

5

‌

C2(100)3(−1)2+

5

‌

C3(100)2(−1)3 +

5

‌

C4(100)(−1)4+

5

‌

C5(−1)5
= 10000000000 – 500000000 + 10000000 – 100000 + 500 – 1 = 9509900499.