To solve this inequality, we first rewrite it in exponential form:

[tex]0.2^{(-1)} \leqslant 5 - x[/tex]

Simplify the left side:

[tex]\frac{1}{0.2} \leqslant 5 - x[/tex]

[tex]5 \leqslant 5 - x[/tex]

Now, we can solve for x:

[tex]5 \leqslant 5 - x[/tex]

[tex]0 \leqslant -x[/tex]

[tex]0 \geqslant x[/tex]

Therefore, the solution to the inequality is:
[tex]x \leqslant 0[/tex]