Distance necessary for stabilizing tire temperature prior to the mileage test on an odometer:

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Tire temperature must reach a stable operating level before a mileage test so the measurements reflect normal, repeatable conditions. When tires are cold, rubber properties and inflation effects can alter rolling resistance and even the effective tire circumference slightly, which affects how far the odometer records for a given distance. Driving about five miles lets the tires heat up and then level off into a steady state, so the readings you get are representative and repeatable for future tests.

Two miles is usually not enough for the tires to fully warm and stabilize, so readings can still be influenced by cold-tire effects. Four miles might be closer, but it can still miss complete stabilization. Ten miles would waste time and might introduce other drift factors, even though the main goal is to have the tires at normal operating temperature. Five miles hits the right balance for reliable stabilization.