Solve for the standard and general equation of the parabola given its different properties. Show all necessary solutions and box your final answer.

1. vertex (5, 3), length of the latus rectum is 12 and opens upward.

2. vertex (2, 6), length of the latus rectum is 15 and opens right.

3. vertex is at the origin; length of the latus rectum is 20 and opens to the left.

4. vertex (-3, 7), focus is at (-3, 4).

5. vertex (1, -5), focus is at (-3, -5)