The electronic structure, chemical bonding, mechanical, and thermal properties of a B-containing mullite Al5BO9 were investigated using a combination of first-principles calculations, Debye model, Clack model, and Slack's equation. The results show that Al5BO9 has a wide band gap of 6.4 eV. The bonding in BO3 triangle and AlO4 tetrahedron is covalent-ionic, whereas that in AlO6 octahedra and AlO5 bipyramids is ionic-covalent. The maximum (245 GPa) and minimum Young's modulus (161 GPa) are along [100] and [010] direction, respectively. Based on the low shear modulus (78 GPa) and low Pugh's ratio (G/B = 0.497), Al5BO9 is predicted as a damage-tolerant ceramic. The most likely slip systems are [010](100) and [100](010). The high Debye temperature (956 K) indicates good high-temperature stability. The minimum thermal conductivity is estimated to be 1.59 W.(m.K)(-1), and the thermal conductivity decreases with temperature as 2071.9/T.