To find the domain of the function $f(x) = \frac{5}{2x + 5}$, we need to determine the values of $x$ for which the function is defined.

Since the function involves a fraction, it is undefined when the denominator is equal to zero. So, we need to solve for $x$ when the denominator equals zero:

$2x + 5 = 0$

Solve for $x$:

$2x = -5$ $x = -\frac{5}{2}$

Thus, the function is undefined at $x = -\frac{5}{2}$. Therefore, the domain of the function is all real numbers except $x = -\frac{5}{2}$.

In interval notation, the domain is: $(-\infty, -\frac{5}{2}) \cup (-\frac{5}{2}, \infty)$

Would you like more details or have any questions?

Here are some related questions:

1. What is the range of the function $f(x) = \frac{5}{2x + 5}$?
2. How do you find the asymptotes of a rational function like $f(x) = \frac{5}{2x + 5}$?
3. What happens to the value of $f(x)$ as $x \to \infty$ or $x \to -\infty$?
4. Can you determine the inverse of the function $f(x) = \frac{5}{2x + 5}$?
5. How does the graph of $f(x) = \frac{5}{2x + 5}$ behave near the point $x = -\frac{5}{2}$?

Tip: When finding the domain of a rational function, always check for values that make the denominator zero!