To determine the value of the fifth term in a series where each term is 10% greater than the previous term, and the first term is 50, follow these steps:

1. **Identify the Series Type**: This series is a geometric sequence, where each term is a fixed percentage greater than the previous term. The common ratio (r) is 1.10, which represents the 10% increase (100% + 10% = 110% = 1.10).

2. **Write the Formula for the \(n\)-th Term**: The formula for the \(n\)-th term \(a_n\) in a geometric sequence is:
\[
a_n = a_1 \times r^{(n-1)}
\]
where \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.

3. **Substitute the Values**: For the fifth term (\(n = 5\)), \(a_1 = 50\) and \(r = 1.10\). Plug these values into the formula:
\[
a_5 = 50 \times (1.10)^{(5-1)}
\]
\[
a_5 = 50 \times (1.10)^4
\]

4. **Calculate \( (1.10)^4 \)**:
\[
(1.10)^4 \approx 1.4641
\]

5. **Find the Fifth Term**:
\[
a_5 = 50 \times 1.4641 \approx 73.21
\]

Thus, the value of the fifth term is approximately $73.21.