find the domain of the function f(x)=5^x-2-3?

4

I suspect your function is
f(x) = 5^(x-2) - 3

The domain is the set of all input values (values for x, in this case), for which the function will be "well-defined" (for any given value in the domain, the function will give one, and only one, clear answer).

5 can be raised to any power (including zero, including negative values, including fractional values, etc.).

There seems to be no restrictions on the domain. No value for x will ever cause a problem.

Therefore, the domain is the set of all real values (from minus infinity, to plus infinity).

a few examples:

f(0) = 5^(0-2) - 3 = 5^(-2) - 3 = (1/5)^2 - 3 = 1/25 - 3 = -2.96
f(2) = 5^(2-2) - 3 = 5^0 - 3 = 1 - 3 = -2
f(pi) = 5^(pi-2) - 3 = 5^(1.14159265358979...) - 3 = 3.27970181...
f(-√2) = 5^(-√2 - 2) - 3 = ... = -2.995892599...