Answer
$|x| \lt 0.56968$
Work Step by Step
The Taylor series for $\sin x $ can be defined as: $\sin x= x-\dfrac{x^3}{3!}+\dfrac{ x^5}{5!}-....$
and $\sin x= x-\dfrac{x^3}{6}+\dfrac{ x^5}{120}-....$
We need to find $ x $.
$\dfrac{|x|^5}{5!} \lt 5 \times 10^{-4} $
or, $|x|^5 \lt 5! \times 5 \times 10^{-4} $
or, $|x| \lt 0.56968$
