A polynomial \(p(x)\) is \(ax^3+8x^2+bx+5\), where \(a\) and \(b\) are integers. It is given that \(2x-1\) is a factor of \(p(x)\) and that a remainder of \(-25\) is obtained when \(p(x)\) is divided by \(x+2\).

(i) Find the value of \(a\) and of \(b\).

(ii) Using your values of \(a\) and \(b\), find the exact solutions of \(p(x)=5\).