5^x^2*16^x-1≥5 inequation

Given the inequality:
$$16^{x} 5^{x^{2}} - 1 \geq 5$$
To solve this inequality, we must first solve the corresponding equation:
$$16^{x} 5^{x^{2}} - 1 = 5$$
Solve:
$$x_{1} = \frac{- \log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$
$$x_{2} = - \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$
$$x_{1} = \frac{- \log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$
$$x_{2} = - \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$
This roots
$$x_{2} = - \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$
$$x_{1} = \frac{- \log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$- \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}} + - \frac{1}{10}$$
=
$$- \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}} - \frac{1}{10}$$
substitute to the expression
$$16^{x} 5^{x^{2}} - 1 \geq 5$$
$$-1 + 16^{- \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}} - \frac{1}{10}} \cdot 5^{\left(- \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}} - \frac{1}{10}\right)^{2}} \geq 5$$

      /                                               2\                                                     
      |/          __________________________         \ |             __________________________              
      ||         /      2         / log(5)\          | |            /      2         / log(5)\               
      ||  1    \/  4*log (2) + log\6      /  + log(4)| |     1    \/  4*log (2) + log\6      /  + log(4) >= 5
      ||- -- - --------------------------------------| |   - -- - --------------------------------------     
      \\  10                   log(5)                / /     10                   log(5)                     
-1 + 5                                                  *16                                                  

one of the solutions of our inequality is:
$$x \leq - \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$

 _____           _____          
      \         /
-------•-------•-------
       x2      x1

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \leq - \frac{\log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$
$$x \geq \frac{- \log{\left(4 \right)} + \sqrt{4 \log{\left(2 \right)}^{2} + \log{\left(6^{\log{\left(5 \right)}} \right)}}}{\log{\left(5 \right)}}$$