log((5-x*))(x+1)<1 inequation

Given the inequality:
$$\left(x + 1\right) \log{\left(5 - x \right)} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(x + 1\right) \log{\left(5 - x \right)} = 1$$
Solve:
$$x_{1} = -0.407508696967762$$
$$x_{2} = 3.76657579329603$$
$$x_{1} = -0.407508696967762$$
$$x_{2} = 3.76657579329603$$
This roots
$$x_{1} = -0.407508696967762$$
$$x_{2} = 3.76657579329603$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-0.407508696967762 + - \frac{1}{10}$$
=
$$-0.507508696967762$$
substitute to the expression
$$\left(x + 1\right) \log{\left(5 - x \right)} < 1$$
$$\left(-0.507508696967762 + 1\right) \log{\left(5 - -0.507508696967762 \right)} < 1$$

0.840245508557916 < 1

one of the solutions of our inequality is:
$$x < -0.407508696967762$$

 _____           _____          
      \         /
-------ο-------ο-------
       x1      x2

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -0.407508696967762$$
$$x > 3.76657579329603$$