Find the sum of the first 6 terms of the geometric sequence $5, \frac{5}{2}, \frac{5}{4}, \ldots$
\[
\mathrm{S}_{6}=\square
\]
(Type an integer or a simplified fraction.)

Step 1 ：We are given a geometric sequence $5, \frac{5}{2}, \frac{5}{4}, \ldots$ and we are asked to find the sum of the first 6 terms.

Step 2 ：The sum of the first n terms of a geometric sequence can be calculated using the formula: \(S_n = a \cdot \frac{1 - r^n}{1 - r}\) where: \(S_n\) is the sum of the first n terms, \(a\) is the first term of the sequence, \(r\) is the common ratio of the sequence, and \(n\) is the number of terms.

Step 3 ：In this case, \(a = 5\), \(r = \frac{1}{2}\), and \(n = 6\). We can substitute these values into the formula to find the sum.

Step 4 ：Substituting the values into the formula, we get: \(S_6 = 5 \cdot \frac{1 - (\frac{1}{2})^6}{1 - \frac{1}{2}}\)

Step 5 ：Solving the above expression, we get \(S_6 = \frac{315}{32}\)

Step 6 ：So, the sum of the first 6 terms of the given geometric sequence is \(\boxed{\frac{315}{32}}\)