Variable $x$ cannot be equal to $5$ since division by zero is not defined. Multiply both sides of the equation by $3\left(x-5\right)$, the least common multiple of $x-5,3$.
$$3\left(x+1\right)=5\left(x-5\right)$$
Use the distributive property to multiply $3$ by $x+1$.
$$3x+3=5\left(x-5\right)$$
Use the distributive property to multiply $5$ by $x-5$.
