Remember that the standard form of a line equation is y = mx + b. Since you need a line that is parallel to y = 5x - 2, the first thing to do is use the same slope (m), which is 5 in this case.
The new line would look like this: y = 5x + b. I use "b" instead of -2, since we'll calculate a "b" for the new line by substituting the given point of (2, -1) into y = 5x + b.
-1 = 5*(2) + b
b = -11
The parallel line that goes through (2,-1) is y = 5x - 11
The new line is the blue, on the right. Note that it is parallel to the original (green) line and also intersects at (2, -1). (Each chart is is 0.5 unit).