1. The problem is to find the indefinite integral of the function $5$ with respect to $x$, i.e., $\int 5 \, dx$. 2. The formula for integrating a constant $a$ with respect to $x$ is: $$\int a \, dx = ax + C$$ where $C$ is the constant of integration. 3. Applying this formula to our problem, we have: $$\int 5 \, dx = 5x + C$$ 4. This means the antiderivative of the constant function $5$ is a linear function $5x$ plus an arbitrary constant $C$. 5. Therefore, the final answer is: $$5x + C$$