To solve the expression \( G = \frac{1}{25} - \frac{4}{27} + \left( -\frac{23}{27} + -\frac{1}{25} - \frac{5}{43} \right) + \frac{5}{43} - \frac{4}{7} \), we will break it down step by step.

First, simplify the expression inside the parentheses:
\[ -\frac{23}{27} + -\frac{1}{25} - \frac{5}{43} \]

Combine the terms inside the parentheses:
\[ -\frac{23}{27} - \frac{1}{25} - \frac{5}{43} \]

Next, add this result to the other terms outside the parentheses:
\[ \frac{1}{25} - \frac{4}{27} + \left( -\frac{23}{27} - \frac{1}{25} - \frac{5}{43} \right) + \frac{5}{43} - \frac{4}{7} \]

Combine like terms:
\[ \frac{1}{25} - \frac{1}{25} - \frac{4}{27} - \frac{23}{27} - \frac{5}{43} + \frac{5}{43} - \frac{4}{7} \]

Notice that \(\frac{1}{25}\) and \(-\frac{1}{25}\) cancel each other out, and \(\frac{5}{43}\) and \(-\frac{5}{43}\) also cancel each other out:
\[ - \frac{4}{27} - \frac{23}{27} - \frac{4}{7} \]

Combine the fractions with the same denominator:
\[ - \left( \frac{4}{27} + \frac{23}{27} \right) - \frac{4}{7} \]

\[ - \frac{27}{27} - \frac{4}{7} \]

\[ -1 - \frac{4}{7} \]

Convert \(-1\) to a fraction with a common denominator of 7:
\[ -1 = -\frac{7}{7} \]

Combine the fractions:
\[ -\frac{7}{7} - \frac{4}{7} = -\frac{11}{7} \]

So, the value of \( G \) is:
\[ G = -\frac{11}{7} \]