b=|AV|=\sqrt{(5\sqrt2)^2+(\frac{5\sqrt3}{3})^2}=\sqrt{5^2\cdot2+\frac{5^2\cdot3}{3^2}}=\sqrt{5^2\cdot 2+\frac{5^2}{3}}=\sqrt{5^2(2+\frac13)}=5\sqrt{\frac73}=\frac{5\sqrt7}{\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}=\boxed{\frac{5\sqrt{21}}{3}}\ cm.