تابع $f(x) = \left\{ \begin{gathered}
\tan \frac{{(2x + 1)\pi }}{4}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \leqslant 1 \hfill \\
\frac{{\left| {{x^2} + x - 2} \right|}}{{a(1 - x)}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1 \lt x \lt 5 \hfill \\
b(x - \left[ { - x} \right])\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \geqslant 5 \hfill \\
\end{gathered} \right.$ روی بازه $\left[ {1,5} \right]$ پیوسته است. مقدار ab کدام است؟