5 The polynomial \(x ^ { 4 } + 5 x + a\) is denoted by \(\mathrm { p } ( x )\). It is given that \(x ^ { 2 } - x + 3\) is a factor of \(\mathrm { p } ( x )\).
- Find the value of \(a\) and factorise \(\mathrm { p } ( x )\) completely.
- Hence state the number of real roots of the equation \(\mathrm { p } ( x ) = 0\), justifying your answer.