#### Answer

The domain of the given function is the set of all real numbers except $\frac{8}{5}$.

#### Work Step by Step

When the question asks for the domain of the function, it is asking for what values of x can be legally substituted into the function. (For instance, in the function $\frac{2}{x}$, x $\ne$ 0, for this would make the denominator of the fraction equal to 0.)
Thus, we look for the number that makes the denominator zero by equating the denominator to 0:
$5x-8=0
\\5x = 0+8
\\5x=8
\\x = \frac{8}{5}$
Thus, when $x=\frac{8}{5}$. the denominator is equal to zero.
Therefore, the domain of the given function is the set of all real numbers except $\frac{8}{5}$.