Your solution looks plausible to me. If we consider the geometry of the problem, we can rewrite the constraints as follows:

- 5*x0 - 4*x1 ≤ -1
- -3*x0 + 7*x1 ≤ 5

and thus also as

- x1 ≥ 1/4 + 5/4*x0 (blue)
- x1 ≤ 5/7 + 3/7*x0 (red)

Hence, solutions are above the blue and below the red line below:

The simplex algorithm starts in (x0,x1) = (0,0) and moves to one of the intersection points. The example solution moves to (x0,x1) = (-1/5,0) and your solution moves to (x0,x1) = (0,1/4) which are both valid solutions.