\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\Rightarrow\frac{x^2}{4}=\frac{y^2}{9}=\frac{z^2}{25}=\frac{x^2+y^2+z^2}{4+9+25}=\frac{a}{38}\)
\(\frac{x}{2}=\frac{a}{38}\Rightarrow x=\frac{a}{19}\)
\(\frac{y}{3}=\frac{a}{38}\Rightarrow y=\frac{3a}{38}\)
\(\frac{z}{5}=\frac{a}{38}\Rightarrow z=\frac{5a}{38}\)