$A=\left[\begin{array}{ccc}K & 5 & 2 \\ 2 & -K & 5 \\ 5 & 2 & -K\end{array}\right]$
$\begin{array}{ll}\therefore & |A|=K\left(K^2-10\right)-5(-2 K-25)+2(4+5 K)=190 \\ \Rightarrow & K^3-10 K+10 K+125+8+10 K=190 \\ \Rightarrow & K^3+10 K-57=0 \Rightarrow(K-3)\left(K^2+3 K+19\right)=0 \\ \Rightarrow & K=3 \\ \therefore & A=\left[\begin{array}{ccc}3 & 5 & 2 \\ 2 & -3 & 5 \\ 5 & 2 & -3\end{array}\right]\end{array}$
$\begin{array}{lll}C_{11}=-1 & C_{21}=19 & C_{31}=31 \\ C_{12}=31 & C_{22}=-19 & C_{32}=-11 \\ C_{13}=19 & C_{23}=19 & C_{33}=-19 \\ \therefore & \text { adj } A=\left[\begin{array}{ccc}-1 & 19 & 31 \\ 31 & -19 & -11 \\ 19 & 19 & -19\end{array}\right]\end{array}$