I see it now. You were correct in your calculations. However, you only considered the dividends from time 5 onward, and you did not discount. Using your approach, you can solve for the price as:
\(S_0 = \dfrac{5}{1.12} + \dfrac{5}{1.12^2}+\dfrac{5}{1.12^3}+\dfrac{5}{1.12^4}+\dfrac{1}{1.12^4}\left(\dfrac{5\times (1-0.25)}{0.12-0.02}\right)\)
I have attached the Excel sheet using your approach