Partners HealthCare System Inc. yesterday posted a more than fivefold increase in its second-quarter operating income, citing factors ranging from a boost in research revenue to higher payments for complex care at its Harvard-affiliated teaching hospitals in Boston. For the three months ending March 31, Partners recorded operating income of $71 million on revenue of $2.1 billion. That was a sharp increase from its $13 million in income on revenue of $1.9 billion for the same period in 2010. Partners' nonoperating income climbed to $95 million last quarter, compared with $9 million a year earlier, largely due to the strong rebound of the health care company's investments in financial markets. Meanwhile, Peter K. Markell, vice president for finance at Partners -- the state's largest hospital and physician network -- said it is still talking with insurers about reopening contracts extending to 2012 or 2013. The goal is to provide rate relief to small businesses.