6.
\(cos\sqrt{x+\dfrac{\pi}{4}}\in\left[-1;1\right]\)
\(\Rightarrow-5\le5cos\sqrt{x+\dfrac{\pi}{4}}\le5\)
\(\Leftrightarrow-5\le y\le5\)
\(\Rightarrow miny=-5\Leftrightarrow cos\sqrt{x+\dfrac{\pi}{4}}=-1\Leftrightarrow\sqrt{x+\dfrac{\pi}{4}}=\pi+k2\pi\Leftrightarrow...\)
\(maxy=5\Leftrightarrow cos\sqrt{x+\dfrac{\pi}{4}}=1\Leftrightarrow\sqrt{x+\dfrac{\pi}{4}}=k2\pi\Leftrightarrow...\)