The Bekenstein-Hawking entropy formula $ S_{BH} = A/4 $ for five-dimensional extremal black holes in string theory is derived by counting the degeneracy of BPS soliton bound states. The paper explores the microscopic origin of black hole entropy by considering phases of string theory with five noncompact dimensions and N = 4 supersymmetry. Black holes in these theories can carry both axion charge $ Q_H $ and electric charge $ Q_F^2 $. Extremal black holes with either $ Q_H = 0 $ or $ Q_F = 0 $ have degenerate horizons with zero area. The paper focuses on BPS states with both $ Q_H $ and $ Q_F $ non-zero, which preserve 1/4 of N = 4 supersymmetry. These states are bound states of minimally-charged BPS solitons, and their degeneracy can be computed topologically. The degeneracy of these states is given by $ S_{stat} = 2\pi\sqrt{Q_H(\frac{1}{2}Q_F^2 + 1)} $, which agrees with the Bekenstein-Hawking entropy $ S_{BH} = 2\pi\sqrt{\frac{Q_H Q_F^2}{2}} $ for large charges. The five-dimensional problem is considered because it is the simplest non-trivial case. The paper also discusses the low-energy effective action and the role of string loop and sigma model perturbations. The results are consistent with the expected Bekenstein-Hawking entropy for large charges. The paper also considers the counting of microscopic BPS states using D-branes and their worldvolume theories. The degeneracy of these states is related to the elliptic genus of a sigma model on a symmetric product of K3 manifolds. The leading degeneracy of the elliptic genus matches the Bekenstein-Hawking entropy for large charges. The paper concludes that the results are consistent with the black hole information puzzle and suggest that further progress is possible in understanding the microscopic origin of black hole entropy.The Bekenstein-Hawking entropy formula $ S_{BH} = A/4 $ for five-dimensional extremal black holes in string theory is derived by counting the degeneracy of BPS soliton bound states. The paper explores the microscopic origin of black hole entropy by considering phases of string theory with five noncompact dimensions and N = 4 supersymmetry. Black holes in these theories can carry both axion charge $ Q_H $ and electric charge $ Q_F^2 $. Extremal black holes with either $ Q_H = 0 $ or $ Q_F = 0 $ have degenerate horizons with zero area. The paper focuses on BPS states with both $ Q_H $ and $ Q_F $ non-zero, which preserve 1/4 of N = 4 supersymmetry. These states are bound states of minimally-charged BPS solitons, and their degeneracy can be computed topologically. The degeneracy of these states is given by $ S_{stat} = 2\pi\sqrt{Q_H(\frac{1}{2}Q_F^2 + 1)} $, which agrees with the Bekenstein-Hawking entropy $ S_{BH} = 2\pi\sqrt{\frac{Q_H Q_F^2}{2}} $ for large charges. The five-dimensional problem is considered because it is the simplest non-trivial case. The paper also discusses the low-energy effective action and the role of string loop and sigma model perturbations. The results are consistent with the expected Bekenstein-Hawking entropy for large charges. The paper also considers the counting of microscopic BPS states using D-branes and their worldvolume theories. The degeneracy of these states is related to the elliptic genus of a sigma model on a symmetric product of K3 manifolds. The leading degeneracy of the elliptic genus matches the Bekenstein-Hawking entropy for large charges. The paper concludes that the results are consistent with the black hole information puzzle and suggest that further progress is possible in understanding the microscopic origin of black hole entropy.