The point goes through the origin, and you can simplify by saying the length of the segment from (0,0) to (5,t) is sqrt(34). Apply Pythagorean theorem to find t, then slope will be t/5.

Edit: There is not enough information. We do not know if t is positive or negative. So we get two possible answers, and can't know which one is true. (I guess just use the sign.)