Mixed Ratio?

$\begin{aligned} x:y=5:2 \rightarrow \color{#D61F06}{\dfrac{x}{y}=\dfrac{5}{2}}\\ y:z=3:2 \rightarrow\color{#3D99F6}{ \dfrac{y}{z}=\dfrac{3}{2}}\\ x:z=\dfrac{x}{z}=\color{#D61F06}{\dfrac{x}{y}}\times\color{#3D99F6}{\dfrac{y}{z}}=\color{#D61F06}{\dfrac{5}{2}}\times\color{#3D99F6}{\dfrac{3}{2}}=\dfrac{15}{4}=\boxed{15:4} \end{aligned}$

$\rightarrow \dfrac{x}{y}=\dfrac{5}{2}$

$\Rightarrow y=\dfrac{2x}{5}$ ..... $(1)$

$\rightarrow \dfrac{y}{z}=\dfrac{3}{2}$

From $(1)$ .

$15z=4x$

$\dfrac{x}{z}=\boxed{\dfrac{15}{4}}$

We make $y$ be lcm(2,3)=6 so that $x:y=15:6$ $y:z=6:4$ $x:y:z=15:6:4$ $\Rightarrow x:z=\boxed{15:4}$

x:y=5:2 *3= 15:6

y:z=3:2 *2= 6:4

Y are the same, then x:z= 15:4