By solving equations 3x + 4y = 23 and 5x + 12y = 39 with the help of cross multiplication method, we obtain `(x)/(a) = (y)/(b) = (1)/(c )`, then find `(a + 4b)/(5c)`.

Answer

To solve the equations \(3x + 4y = 23\) and \(5x + 12y = 39\) using the cross multiplication method, we can follow these steps:

### Step 1: Write the equations in standard form
The given equations are already in standard form:
1. \(3x + 4y = 23\) (Equation 1)
2. \(5x + 12y = 39\) (Equation 2)

### Step 2: Identify coefficients
From the equations, we can identify the coefficients:
- For Equation 1: \(a_1 = 3\), \(b_1 = 4\), \(c_1 = 23\)
- For Equation 2: \(a_2 = 5\), \(b_2 = 12\), \(c_2 = 39\)

### Step 3: Apply the cross multiplication method
Using the cross multiplication method, we have:
\[ \frac{x}{b_1 c_2 - b_2 c_1} = \frac{y}{a_1 c_2 - a_2 c_1} = \frac{1}{a_1 b_2 - a_2 b_1} \]

### Step 4: Calculate the determinants
1. Calculate \(b_1 c_2 - b_2 c_1\):
\[ b_1 c_2 - b_2 c_1 = 4 \cdot 39 - 12 \cdot 23 = 156 - 276 = -120 \]

2. Calculate \(a_1 c_2 - a_2 c_1\):
\[ a_1 c_2 - a_2 c_1 = 3 \cdot 39 - 5 \cdot 23 = 117 - 115 = 2 \]

3. Calculate \(a_1 b_2 - a_2 b_1\):
\[ a_1 b_2 - a_2 b_1 = 3 \cdot 12 - 5 \cdot 4 = 36 - 20 = 16 \]

### Step 5: Set up the ratios
Now we can set up the ratios:
\[ \frac{x}{-120} = \frac{y}{2} = \frac{1}{16} \]

From this, we can identify:
- \(a = -120\)
- \(b = 2\)
- \(c = 16\)

### Step 6: Calculate \(\frac{a + 4b}{5c}\)
Now we need to find:
\[ \frac{a + 4b}{5c} \]
Substituting the values of \(a\), \(b\), and \(c\):
\[ \frac{-120 + 4 \cdot 2}{5 \cdot 16} = \frac{-120 + 8}{80} = \frac{-112}{80} = \frac{-14}{10} = -\frac{7}{5} \]

### Final Answer
Thus, the required value is:
\[ -\frac{7}{5} \]