Answer
$|x| \lt 0.56968$
Work Step by Step
Recall the Taylor series for $\sin x= x-\dfrac{x^3}{3!}+\dfrac{ x^5}{5!}-....$ and $\sin x= x-\dfrac{x^3}{6}+\dfrac{ x^5}{120}-....$
We will compute $ x $.
$\dfrac{|x|^5}{5!} \lt 5 \times 10^{-4} $
$\implies |x|^5 \lt 5 \times 4 \times 3 \times 2 \times 1 \times 5 \times 10^{-4} $
$\implies |x| \lt 0.56968$