$\frac{3}{7} \cdot \frac{5}{4}=$

Step 1 ：The problem is asking for the product of two fractions. To find this, we multiply the numerators (the top numbers) together to get the new numerator, and multiply the denominators (the bottom numbers) together to get the new denominator.

Step 2 ：First, identify the numerators and denominators of the fractions. For the fraction \(\frac{3}{7}\), the numerator is 3 and the denominator is 7. For the fraction \(\frac{5}{4}\), the numerator is 5 and the denominator is 4.

Step 3 ：Next, multiply the numerators together to get the new numerator. So, \(3 \times 5 = 15\).

Step 4 ：Then, multiply the denominators together to get the new denominator. So, \(7 \times 4 = 28\).

Step 5 ：Therefore, the product of \(\frac{3}{7}\) and \(\frac{5}{4}\) is \(\frac{15}{28}\).

Step 6 ：Final Answer: \(\boxed{\frac{15}{28}}\)