Use long division to divide. Express any numbers as integers or simplified fractions. \( \left(x^{5}-6 x^{4}+13 x^{3}-8 x+150\right) \div\left(x^{2}-5\right)=\square \)

To divide \( x^{5}-6 x^{4}+13 x^{3}-8 x+150 \) by \( x^{2}-5 \) using long division, set it up as follows: 1. Divide the leading term of the dividend \( x^5 \) by the leading term of the divisor \( x^2 \) to get \( x^3 \). 2. Multiply \( x^3 \) by the entire divisor \( x^2-5 \) to get \( x^5 - 5x^3 \). 3. Subtract this from the original polynomial, leading to a new polynomial: \[ (-6x^4 + 13x^3 - 8x + 150) - (-5x^3) = -6x^4 + 18x^3 - 8x + 150 \] 4. Repeat the process: Divide \( -6x^4 \) by \( x^2 \), which gives \( -6x^2 \). Multiply and subtract, continuing until the degree of the remainder is less than the degree of the divisor. Following through this method gives: The result of the division is: \[ x^3 - 6x^2 + 18x + 82 + \frac{70}{x^2-5} \] So, the answer is: \[ x^3 - 6x^2 + 18x + 82 + \frac{70}{x^2-5} \]