Triangle \(ABC\) is a right triangle with a side length \(\left\lvert\overline{AC}\right\rvert=5, \angle C = 90^\circ\) and the measures of \(\angle A\) and \(\angle B\) unknown. If \(D\) is a point on \(\overline{AB}\) such that \(\angle ADC = 90^\circ\) and \(\left\lvert\overline{AD}\right\rvert=4,\) what is \(\left\lvert\overline{BC}\right\rvert?\)

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