The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3.

Let the radii of two cylinders be $2 r$ and $3 r$, respectively, and their heights $b e 5 h$ and $3 h$, respectively.

Let $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ be the curved surface areas of the two cylinder.

$\mathrm{S}_{1}=$ Curved surface area of the cylinder of height $5 h$ and radius $2 r$

$\mathrm{S}_{2}=$ Curved surface area of the cylinder of height $3 h$ and radius $3 r$

$\therefore \mathrm{S}_{1}: \mathrm{S}_{2}=2 \times \pi \times r \times h: 2 \times \pi \times r \times h$

$=\frac{2 \times \pi \times 2 r \times 5 h}{2 \times \pi \times 3 r \times 3 h}$

$=10: 9$