Divide the polynomial $5x^4-3x^2+2x-7$ by the polynomial $x^2-1$.

Step 1 ：First, write the division as a fraction: $\frac{5x^4-3x^2+2x-7}{x^2-1}$.

Step 2 ：Next, perform the polynomial division. Divide the first term of the numerator by the first term of the denominator to get the first term of the quotient, which is $5x^2$. Multiply the entire denominator by $5x^2$ and subtract the result from the numerator to get a new numerator.

Step 3 ：The new numerator is $5x^4-5x^2-3x^2+2x-7=0x^3+2x^2+2x-7$. Repeat the process with the new numerator, getting the second term of the quotient $2x$, and subtracting the result from the new numerator to get a new numerator.

Step 4 ：The new numerator is $2x^2-2x+2x-7=0x+0$.

Step 5 ：This means the quotient is $5x^2+2x$ and the remainder is $-7$.

Step 6 ：So, the result of the division is $5x^2+2x-\frac{7}{x^2-1}$.