Use synthetic division to find the quotient and remainder when $-x^{3}-5 x^{2}+3$ is divided by $x+5$ by completing the parts below
(a) Complete this synthetic division table.
(b) Write your answer in the following form: Quotient $+\frac{\text { Remainder }}{x+5}$.
\[
\frac{-x^{3}-5 x^{2}+3}{x+5}=\square+\frac{\square}{x+5}
\]

Step 1 ：Set up the synthetic division using the coefficients of the polynomial \(-x^{3}-5 x^{2}+3\) and the root of the divisor \(x+5\), which is \(-5\).

Step 2 ：Perform the synthetic division process: bring down the first coefficient, multiply it by the root, add it to the next coefficient, and repeat until all coefficients have been processed.

Step 3 ：The last number obtained is the remainder, and the rest are the coefficients of the quotient polynomial.

Step 4 ：The quotient is \(-x^{2}\) and the remainder is \(3\).

Step 5 ：So, the division of \(-x^{3}-5 x^{2}+3\) by \(x+5\) can be written as \(-x^{2} + \frac{3}{x+5}\).

Step 6 ：\(\boxed{\frac{-x^{3}-5 x^{2}+3}{x+5}=-x^{2}+\frac{3}{x+5}}\)