Walk the grid

Probability Level 5

You start at the point (x,y)=(1,1)(x,y) = (1,1) in a Cartesian coordinate system.

Every second you move randomly 1 unit either up, down, left or right.

What is the expected value for the number of seconds it will take for you to land on a point (5m,5n)(5m, 5n) where mm and nn are integers?

Clarification: You can walk anywhere in all four quadrants of the Cartesian coordinate system. mm and/or nn can be negative.

Image credit: clipartfreefor.com

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