5.
\((1)\)不等式\(\Delta ABD\)的解集为________.
\((2)\)若数列\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项和为\({{S}_{n}}=\dfrac{2}{3}{{a}_{n}}+\dfrac{1}{3},\)则数列\(\left\{ {{a}_{n}} \right\}\)的通项公式是\({{a}_{n}}=\)_______.
\((3)\)在\(\Delta ABC\)中,角\(A,B,C\)的对边分别为\(a,b,c,\)且\({{a}^{2}}=b(b+c),\)则\(\dfrac{B}{A}{=}\)_______.
\((4)\)在平面四边形\(ABCD\)中,连接对角线\(BD\),已知\(CD=9\),\(BD=16\),\(∠BDC=90^{\circ},\sin A= \dfrac{4}{5}, \)则对角线\(AC\)的最大值为________.