The densities of two substances are in the ratio `5 : 6` and the specific heats are in the ratio `3:5` respectively. The ratio of their thermal capacities per unit volume is

Answer

To solve the problem, we need to find the ratio of the thermal capacities per unit volume of two substances given their densities and specific heats.

### Step-by-Step Solution:

1. **Understand the Given Ratios**:
- The ratio of the densities of the two substances is given as:
\[ \frac{\rho_1}{\rho_2} = \frac{5}{6} \]
- The ratio of the specific heats of the two substances is given as:
\[ \frac{S_1}{S_2} = \frac{3}{5} \]

2. **Define Thermal Capacity**:
- The thermal capacity \( H \) of a substance is defined as:
\[ H = m \cdot S \]
- Where \( m \) is the mass and \( S \) is the specific heat.

3. **Express Mass in Terms of Density and Volume**:
- The mass \( m \) can be expressed in terms of density \( \rho \) and volume \( V \):
\[ m = \rho \cdot V \]
- Thus, the thermal capacity for each substance can be expressed as:
\[ H_1 = \rho_1 \cdot V_1 \cdot S_1 \]
\[ H_2 = \rho_2 \cdot V_2 \cdot S_2 \]

4. **Calculate Thermal Capacity per Unit Volume**:
- The thermal capacity per unit volume for each substance is given by:
\[ \frac{H_1}{V_1} = \frac{\rho_1 \cdot S_1}{V_1} \]
\[ \frac{H_2}{V_2} = \frac{\rho_2 \cdot S_2}{V_2} \]

5. **Find the Ratio of Thermal Capacities per Unit Volume**:
- The ratio of thermal capacities per unit volume is:
\[ \frac{\frac{H_1}{V_1}}{\frac{H_2}{V_2}} = \frac{\rho_1 \cdot S_1}{\rho_2 \cdot S_2} \]

6. **Substitute the Given Ratios**:
- Substitute the known ratios into the equation:
\[ \frac{H_1/V_1}{H_2/V_2} = \frac{\rho_1}{\rho_2} \cdot \frac{S_1}{S_2} = \frac{5/6}{3/5} \]

7. **Simplify the Expression**:
- Simplifying the expression:
\[ \frac{5}{6} \cdot \frac{5}{3} = \frac{25}{18} \]

8. **Final Ratio**:
- Therefore, the ratio of their thermal capacities per unit volume is:
\[ \frac{H_1/V_1}{H_2/V_2} = \frac{25}{18} \]

### Conclusion:
The ratio of their thermal capacities per unit volume is \( \frac{25}{18} \).