Given Information:
- Point: (-2,5)
- Equation of line: 4x + y - 19 = 0

Step 1: Find the slope of the given line
To find the slope of the given line, we need to rearrange the equation of the line into slope-intercept form (y = mx + b), where m represents the slope.
Rearranging the equation, we have:
y = -4x + 19
Comparing this with the slope-intercept form, we can see that the slope (m) of the given line is -4.

Step 2: Find the slope of the line perpendicular to the given line
The slope of a perpendicular line is the negative reciprocal of the slope of the given line. In this case, the slope of the perpendicular line is the negative reciprocal of -4.
Therefore, the slope of the perpendicular line is 1/4.

Step 3: Use the point-slope form to find the equation of the perpendicular line
The point-slope form of a line is given by:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line and m is the slope of the line.
Substituting the given point (-2,5) and the slope 1/4 into the point-slope form, we have:
y - 5 = 1/4(x - (-2))
Simplifying this equation, we get:
y - 5 = 1/4(x + 2)

Step 4: Convert the equation to standard form
To convert the equation to standard form (Ax + By = C), we need to eliminate the fraction by multiplying through by 4:
4(y - 5) = x + 2
4y - 20 = x + 2
Rearranging the terms, we have:
x - 4y = -22

Step 5: Final Equation
The equation of the line passing through the point (-2,5) and perpendicular to the line 4x + y - 19 = 0 is:
x - 4y = -22