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\[\sqrt{(x+3)^2+(5-20)^2}=17\]

\[ \sqrt{(x+3)^2+225}=17\]

\[(x+3)^2+225=17\]

\[(x+3)^2=64\]

\[\pm\sqrt{(x+2)^2}=\sqrt{64}\]

\[x+3=8\text{ or } -x-3=8\]

Therefore,

\[x=5 \text{ or } x=-11\]

\[x=max(5,-11)=5\]

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