To solve the system of equations you've presented, let's first rewrite them clearly:

1. \( \frac{4x - 1}{3} \leq 2 \)
2. \( \frac{2x - 1}{2x + 5} = -\sqrt{15x} \)
3. \( 2y + 3 = -1 \quad \text{and} \quad y + 1 = 5 \)

### Step 1: Solve each equation

**Equation 1:**
\[ \frac{4x - 1}{3} \leq 2 \]

Multiply both sides by 3:
\[ 4x - 1 \leq 6 \]

Add 1 to both sides:
\[ 4x \leq 7 \]

Divide by 4:
\[ x \leq \frac{7}{4} \]

**Equation 2:**
\[ \frac{2x - 1}{2x + 5} = -\sqrt{15x} \]

Cross-multiply:
\[ 2x - 1 = -\sqrt{15x}(2x + 5) \]

This equation is more complex and may require rearrangement and squaring both sides to eliminate the square root. This leads to a quadratic equation.

**Equation 3:**
1. \( 2y + 3 = -1 \)
\[ 2y = -4 \]
\[ y = -2 \]

2. \( y + 1 = 5 \)
\[ y = 4 \]

So there is a contradiction in solving for \(y\). We need further implications based on the context.

### Final Solution
For the first equation, we have \( x \leq \frac{7}{4} \) from the first equation. The second equation needs further development based on values of \(x\). The system indicates there might be constraints on possible values of \(x\).

To fully solve the second equation, further numerical methods may be necessary, depending on any additional constraints provided in the original problem statement.

Therefore, the probable solutions:
- For \( x \): \( x \leq \frac{7}{4} \)
- For \( y \): There is an inconsistency in the values resulting from the third equation.

To finalize, could you clarify if there are specific parameters or methods (like numerical or graphical) you would like to explore?