The intercepts cut off by the plane 7x+ y - z = 5 are `(5)/(7), -5,`5.

Answer

To find the intercepts cut off by the plane given by the equation \(7x + y - z = 5\), we will determine the x-intercept, y-intercept, and z-intercept step by step.

### Step 1: Finding the x-intercept
To find the x-intercept, we set \(y = 0\) and \(z = 0\) in the equation of the plane.

\[ 7x + 0 - 0 = 5 \]

This simplifies to:

\[ 7x = 5 \]

Now, solving for \(x\):

\[ x = \frac{5}{7} \]

### Step 2: Finding the y-intercept
Next, we find the y-intercept by setting \(x = 0\) and \(z = 0\) in the equation of the plane.

\[ 7(0) + y - 0 = 5 \]

This simplifies to:

\[ y = 5 \]

### Step 3: Finding the z-intercept
Finally, we find the z-intercept by setting \(x = 0\) and \(y = 0\) in the equation of the plane.

\[ 7(0) + 0 - z = 5 \]

This simplifies to:

\[ -z = 5 \]

Thus, solving for \(z\):

\[ z = -5 \]

### Final Result
The intercepts cut off by the plane \(7x + y - z = 5\) are:

- x-intercept: \(\frac{5}{7}\)
- y-intercept: \(5\)
- z-intercept: \(-5\)

So, the intercepts are \(\left(\frac{5}{7}, 5, -5\right)\).

---