To solve the expression \(0.275 + \left(-\frac{8}{15}\right) + \frac{29}{40} + \left(-\frac{9}{17}\right) - 1 \frac{1}{3}\), we need to handle both the fractions and the mixed number. Let's break it down step by step:

1. **Convert the mixed number to an improper fraction:**
\(1 \frac{1}{3} = \frac{4}{3}\)

2. **Convert all numbers to a common format (decimals or fractions):**
- \(0.275\) is already a decimal.
- \(-\frac{8}{15}\) can be converted to a decimal: \(-\frac{8}{15} \approx -0.5333\)
- \(\frac{29}{40}\) can be converted to a decimal: \(\frac{29}{40} = 0.725\)
- \(-\frac{9}{17}\) can be converted to a decimal: \(-\frac{9}{17} \approx -0.5294\)
- \(\frac{4}{3}\) can be converted to a decimal: \(\frac{4}{3} \approx 1.3333\)

3. **Add/Subtract the decimals:**
\[
0.275 + (-0.5333) + 0.725 + (-0.5294) - 1.3333
\]

4. **Perform the arithmetic operations:**
\[
0.275 - 0.5333 = -0.2583
\]
\[
-0.2583 + 0.725 = 0.4667
\]
\[
0.4667 - 0.5294 = -0.0627
\]
\[
-0.0627 - 1.3333 = -1.396
\]

So, the result of the expression \(0.275 + \left(-\frac{8}{15}\right) + \frac{29}{40} + \left(-\frac{9}{17}\right) - 1 \frac{1}{3}\) is approximately \(-1.396\).