(1/2)^x-5 = 16^x

1/2 = 2^(- 1)

16 = 2^4

2^(5 - x) = 2^4x

5 - x = 4x

5 = 5x

x = 1

Проверка: (1/2)^(- 4) = 16

2^4 = 16

Ответ: x = 1.