Consider the following recurrence relation: F$($n$)=8*$F$($n$-1)+4*$F$($n$-2)+7*$F$($n$-3)-2*$F$($n$-4)+3*$F$($n$-5)-4*$F$($n$-6)-8*$F$($n$-7)+0*$F$($n$-8)+7*$F$($n$-9)-7*$F$($n$-10).$ The final characteristic polynomial equation set to zero $($right before computing the roots$)$ has what number in front of the term that is raised to the fifth power? The answer MUST supply digits only and if negative, then start with the minus sign.