India's private sector growth eased in May as a manufacturing slowdown driven by the Middle East war and cooling international demand offset a marginal pick-up in the service economy, a survey showed. * The HSBC flash Composite Purchasing Managers' Index (PMI), compiled by S&P Global, dipped to 58.1 this month from April's final reading of 58.2, but was higher than a Reuters poll median forecast for 58.0. The 50-mark separates expansion from contraction. * May's deceleration was primarily centred in manufacturing, where new orders expanded at one of the slowest rates in nearly four years and production growth eased to its second-weakest level since mid-2022. The factory PMI dropped to 54.3 in May from April's 54.7.