A real battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected to an ideal high-resistance digital voltmeter. When only the voltmeter is connected across the battery terminals, the reading is \(12\text{ V}\). When a resistor with resistance \(R = 5.0\text{ }\Omega\) is connected in parallel across the terminals, the voltmeter reading drops to \(10\text{ V}\). What is the internal resistance \(r\) of the battery?