* HK->Shanghai Connect daily quota used -1.4%, Shanghai->HK daily quota used 1.3% * FTSE China A50 -1.3% SHANGHAI, May 28 (Reuters) - China’s major stock indexes slipped on Monday after the country’s factory activity slowed slightly in May, but were on track for best monthly gain in about six months. ** The CSI300 index fell 0.5% to 5,296.53 points at the end of the morning session, while the Shanghai Composite Index lost 0.2% to 3,593.61 points. ** Shenzhen’s start-up board ChiNext added 1.6%, while Shanghai’s tech-focused STAR50 index climbed 3.1%. ** The CSI new energy index rose 3.4%, while the CSI300 transport index and the CSI300 consumer discretionary index fell 1.8% and 1.9%, respectively.