(3x² + 5) / (5x² + 5x)

Factor out the common term $5x$:

$$5x(x + 1) = 0$$

$$5x = 0 \implies x = 0$$ $$x + 1 = 0 \implies x = -1$$

These are the values of $x$ for which the denominator is zero. Therefore, these values must be excluded from the domain.

The domain of the function is all real numbers except $x=0$ and $x=-1$.
In set-builder notation:

$$\boxed{\left\{x \in \mathbb{R} \mid x \neq -1, x \neq 0\right\}}$$

In interval notation:

$$\boxed{\left(-\infty, -1\right) \cup \left(-1, 0\right) \cup \left(0, \infty\right)}$$