Statement-1 The distance between the planes `4x-5y+3z=5 and 4x-5y+3z+2=0` is `(3)/(5sqrt(2))`.
Statement-2 The distance between `ax+by+cz+d_1=0` and `ax+by+cz+d_2=0` is `|(d_1-d_2)/(sqrt(a^2+b^2+c^2))|`.

Options

A. Statement 1 is true, Statement 2 is also true, Statement-2 is the correct explanation of Statement-1.
B. Statement 1 is true, Statement 2 is also true, Statement-2 is not the correct explanation of Statement-1.
C. Statement 1 is true, Statement 2 is false.
D. Statement 1 is false, Statement 2 is true

Answer

To solve the problem, we need to analyze the two statements regarding the distance between planes in a three-dimensional coordinate system.

### Step-by-Step Solution:

1. **Identify the Planes**:
The equations of the planes given in Statement 1 are:
- Plane 1: \( 4x - 5y + 3z = 5 \)
- Plane 2: \( 4x - 5y + 3z + 2 = 0 \)

We can rewrite Plane 1 as:
\[ 4x - 5y + 3z - 5 = 0 \]
Thus, we have:
- Plane 1: \( 4x - 5y + 3z - 5 = 0 \) (where \( d_1 = -5 \))
- Plane 2: \( 4x - 5y + 3z + 2 = 0 \) (where \( d_2 = 2 \))

2. **Check if the Planes are Parallel**:
The planes are parallel if the coefficients of \( x \), \( y \), and \( z \) are proportional. Here, both planes have the same coefficients:
- Coefficient of \( x \): \( 4 \)
- Coefficient of \( y \): \( -5 \)
- Coefficient of \( z \): \( 3 \)

Since the coefficients are the same, the planes are indeed parallel.

3. **Use the Distance Formula**:
The distance \( D \) between two parallel planes given by the equations \( ax + by + cz + d_1 = 0 \) and \( ax + by + cz + d_2 = 0 \) is given by:
\[ D = \frac{|d_1 - d_2|}{\sqrt{a^2 + b^2 + c^2}} \]
Here, \( a = 4 \), \( b = -5 \), \( c = 3 \), \( d_1 = -5 \), and \( d_2 = 2 \).

4. **Calculate the Numerator**:
\[ |d_1 - d_2| = |-5 - 2| = |-7| = 7 \]

5. **Calculate the Denominator**:
\[ \sqrt{a^2 + b^2 + c^2} = \sqrt{4^2 + (-5)^2 + 3^2} = \sqrt{16 + 25 + 9} = \sqrt{50} = 5\sqrt{2} \]

6. **Calculate the Distance**:
Now substituting the values into the distance formula:
\[ D = \frac{7}{5\sqrt{2}} \]

7. **Conclusion**:
The calculated distance between the two planes is:
\[ D = \frac{7}{5\sqrt{2}} \]
This contradicts Statement 1, which claims the distance is \( \frac{3}{5\sqrt{2}} \). Therefore, Statement 1 is false.

8. **Verify Statement 2**:
Statement 2 is a general formula for the distance between two parallel planes, which we have verified to be correct. Thus, Statement 2 is true.

### Final Answer:
- Statement 1 is false.
- Statement 2 is true.