Apply Pascal's principle for an ideal hydraulic lift.

Pascal's principle states that the pressure exerted on an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of the container. Therefore, the pressure at the input piston ($P_1$) is equal to the pressure at the output piston ($P_2$).

$$P_1 = P_2$$

Since pressure $P = \frac{F}{A}$, we can write:

$$\frac{F_1}{A_1} = \frac{F_2}{A_2}$$

We are given that $A_2 = 25A_1$. Substitute this into the equation from Step 1:

$$\frac{F_1}{A_1} = \frac{F_2}{25A_1}$$

To find $F_2$, multiply both sides of the equation by $25A_1$:

$$F_2 = \frac{F_1}{A_1} \times 25A_1$$ $$F_2 = 25F_1$$

The output force $F_2$ is $25F_1$.