#### Answer

quotient $2x^2-4x+1$, remainder $-10$

#### Work Step by Step

Step 1. Using long division as shown in the figure, we have $\frac{10x^3-26x^2+17x-13}{5x-3}=2x^2-4x+1+\frac{-10}{5x-3}$
Step 2. We can identify the quotient as $2x^2-4x+1$ and the remainder as $-10$