To solve the given expressions, let's break them down step by step.

### Problem 15:
Expression:
\[ A = \sqrt{(\sqrt{5} - 3)^3} + \frac{4}{\sqrt{5} - 3} \]

### Problem 16:
Expression:
\[ A = \frac{5 + 2\sqrt{5}}{\sqrt{5}} + \sqrt{(3 - \sqrt{5})^2} \]

Let's start solving them one by one:

### Problem 15:
1. Simplify \(\sqrt{(\sqrt{5} - 3)^3}\):
\[ (\sqrt{5} - 3)^3 = (\sqrt{5} - 3)(\sqrt{5} - 3)(\sqrt{5} - 3) \]
2. For ease of calculation, write \((\sqrt{5} - 3)\) as a simpler term and then cube it:
\[ = (\sqrt{5} - 3)^{3/2} \times (\sqrt{5} - 3) = \sqrt{(\sqrt{5} - 3)^2}(\sqrt{5} - 3) = (\sqrt{5} - 3)(\sqrt{5} - 3) = 5 - 6\sqrt{5} + 9 = 14 - 6\sqrt{5} \]

3. Simplify the next term:
\[ \frac{4}{\sqrt{5} - 3} \]
Rationalize the denominator:
\[ \frac{4}{\sqrt{5} - 3} \cdot \frac{\sqrt{5} + 3}{\sqrt{5} + 3} = \frac{4(\sqrt{5} + 3)}{5 - 9} = \frac{4(\sqrt{5} + 3)}{-4} = -(\sqrt{5} + 3) = -\sqrt{5} - 3 \]

Putting it together:
\[ A = \sqrt{14 - 6\sqrt{5}} + (-\sqrt{5} - 3) = 0 \]

### Problem 16:
1. First term: \(\frac{5 + 2\sqrt{5}}{\sqrt{5}}\):
\[ \frac{5 + 2\sqrt{5}}{\sqrt{5}} = \frac{5}{\sqrt{5}} + \frac{2\sqrt{5}}{\sqrt{5}} = \sqrt{5} + 2 \]

2. Second term: \(\sqrt{(3 - \sqrt{5})^2}\):
\[ \sqrt{(3 - \sqrt{5})^2} = |3 - \sqrt{5}| = 3 - \sqrt{5} \ (since \ 3 > \sqrt{5}) \]

Combining the terms:
\[ A = (\sqrt{5} + 2) + (3 - \sqrt{5}) = 2 + 3 = 5 \]

Thus, the results are:
- For problem 15: \( A = 0 \)
- For problem 16: \( A = 5 \)