The image was too big so I had to share through google drive.
If I got stuck on this question I would first look at the question . I will make sure its center at zero and set the (x-5) equal to zero and find the point (5,-5).I will then find the derivative of y = Ck X^K. Find the first and second derivative. Then solve for the Left side. Then I would have to plug everything back into the original equation. Then simplify that equation. Once I have that I need everything to have the same exponent and k = 0. Then everything that is not having the exponent K and the K=0 I will shift up the right mount. Once everything is the same, I will simplify the equation. Then I would solve for Ck+2. That means I will move everything thats near Ck+2 on the other side. I will then simplify that. Now I will plug in variables for K to get C0,C1,C2,C3,C4. I will make sure everything is in C1 and C0 form. Then for the last part I will plug y(0) = 1 for where has C0 and y'(0)=3 where C1 is. I will get the first 5 terms.