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To find the value of \(x\) in the equation \(x \cdot -2 + 7 = x - 7 \cdot 5\), we need to simplify and solve for \(x\). Here's how we can do it step by step:

1. Simplify both sides of the equation:
   • Left side: \(x \cdot -2 + 7\) simplifies to \(-2x + 7\)
   • Right side: \(x - 7 \cdot 5\) simplifies to \(x - 35\)

So the equation becomes:
$\(-2x + 7 = x - 35\)$

2. Move all terms with \(x\) to one side and constants to the other side:

   • Add \(2x\) to both sides:
     $\(-2x + 7 + 2x = x - 35 + 2x\)$
     $\(7 = 3x - 35\)$
   • Add \(35\) to both sides:
     $\(7 + 35 = 3x - 35 + 35\)$
     $\(42 = 3x\)$

3. Solve for \(x\) by dividing both sides by 3:
   $\(\frac{42}{3} = \frac{3x}{3}\)$
   $\(14 = x\)$

So, the value of \(x\) is 14.

Final Answer:
$\(x = 14\)$