* Exports drop 2.4 percent, imports climb 1.7 percent in May * German industrial production falls 1 percent * Germany suffering from euro crisis, slowdown in China By Michelle Martin BERLIN, July 8 (Reuters) - German exports fell the most since late 2009 in May and industrial output tumbled, suggesting Europe's largest economy is struggling to regain traction, although a rise in imports pointed to robust domestic demand. Combined with last week's figures showing a sharp drop in industrial orders and contraction in the manufacturing sector, the data underscores how much Germany is suffering from weaker demand in Europe and now in China, too. "May's German industrial and trade data are a blow to hopes that a strong recovery in the euro zone's largest economy might soon pull the region out of recession," said Jennifer McKeown, senior European economist at Capital Economics. A bastion of strength in the early years of the euro zone crisis, the German economy shrank in late 2012 and had a subdued start to 2013, narrowly avoiding a recession thanks to private consumption. Exports, traditionally the backbone of the German economy, dropped a seasonally adjusted 2.4 percent in May, data from the Federal Statistics Office showed, far more than the consensus forecast in a Reuters poll for a 0.4 percent drop and double the weakest estimate for a 1.2 percent fall. Shipments to the euro zone, where Germany sends 40 percent of its goods, fell 9.6 percent in May compared with the same month last year. Exports to countries outside Europe slipped 1.6 percent, with a slowdown in China reducing appetite in the country many German firms had looked to as an alternative. "German exports dropped sharply in May, illustrating that the economy still has difficulties to shift into a higher gear," said Carsten Brzeski, senior economist at ING, adding that this was due to calendar effects and weaker demand from China. A purchasing managers' survey published last week suggested that the export situation had not improved by June, when bookings from abroad, especially Asia and elsewhere in Europe, dropped in the manufacturing sector for a fourth straight month.DECLINE IN OUTPUT Industrial output slid by 1 percent in May, twice as much as forecast and the biggest fall since October, as factories produced fewer capital goods and the construction industry stuttered, data from the Economy Ministry showed. Economists said this was partly a correction after the previous month's upwardly revised 2 percent gain and partly due to the high number of public holidays in May and winter weather. The ministry said the overall trend remained positive. McKeown said net trade looked likely to make a big negative contribution to gross domestic product in the second quarter. The government expects exports to be a drag on GDP this year and is relying on private consumption, helped by higher wages, a robust labour market and moderate inflation, to support growth. A 1.7 percent rise in imports will therefore be welcome news for the government as it shows Germans are buying more goods from abroad. "The strength in imports shows domestic demand is robust, which is good for German growth because consumption and investment could make positive contributions to GDP," said Christian Schulz at Berenberg Bank. The rise in imports, which overshot even the highest estimate in a Reuters poll for a 1.2 percent increase, also offers hope to struggling euro zone states seeking to export their way out of their downturns. Recent German non-industrial data has been fairly positive, with sentiment surveys improving, the private sector expanding, joblessness falling and retail sales rising. The seasonally adjusted trade surplus narrowed to 14.1 billion euros from a downwardly revised 17.5 billion in April. The consensus forecast was for a fall to 17.5 billion euros. The German economy is still outperforming peers within the euro zone. France's trade deficit with the rest of the world widened sharply in May, while Spain's industrial output fell for the 21st month in a row.