Let be a function that is defined for all values of in such that is a real number. How many distinct

Let  $$f(x)=\left\lfloor\left(-\frac58\right)^x\right\rfloor$$ be a function that is defined for all values of $x$ in $[0,\infty)$ such that $f(x)$ is a real number. How many distinct values exist in the range of $f(x)$?