Classify the differential equation y'' + 4y' - 5y = 0 by order and linearity.

Step 1: Identify the highest derivative.

The differential equation is:
y'' + 4y' - 5y = 0

The derivatives present are y' and y''.

The highest derivative is y'', which is the second derivative.

Therefore, the equation is a second-order differential equation.

Step 2: Check whether the equation is linear.

A differential equation is linear if the dependent variable y and its derivatives appear only to the first power and are not multiplied by one another.

In this equation, y'', y', and y all appear to the first power. There are no terms such as y^2, (y')^2, yy', or nonlinear functions of y.

Therefore, the equation is linear.

Step 3: State the classification.

The equation is a second-order linear differential equation.