June 21 (Reuters) - LegalZoom is aiming for a valuation of more than $5 billion in its U.S. initial public offering (IPO), marking the online legal services company"s second attempt at a stock market listing, according to a regulatory filing on Monday. The company, co-founded by former O.J. Simpson attorney Robert Shapiro, plans to sell a little more than 19 million shares priced at between $24 and $27 apiece, raising $516 million at the top end of the range. Glendale, California-based LegalZoom filed for an IPO in 2012 but later postponed the offering and withdrew it after two years. LegalZoom was started in 2001 to help people draw up legal documents such as wills, incorporations and trademarks without lawyers and the fees that come with such advice. It raised $500 million in a funding round led by Francisco Partners and GPI Capital in 2018, valuing the company at $2 billion. The investment also included participation from one or more Franklin Templeton Investments funds and funds managed by Neuberger Berman Investment Advisers. In 2014, European private equity firm Permira acquired between 47% and 50% of the company for $200 million, a deal that valued LegalZoom at $425 million at the time. LegalZoom co-founder Shapiro is famous for being part of O.J. Simpson"s legal defense team. He worked on the case with Robert Kardashian, the late father of celebrity Kim Kardashian. Separately, Intapp Inc, a software provider for professional services and capital markets firms, said on Monday it would raise $294 million in its IPO, aiming for a valuation of about $1.65 billion. Intapp, whose products range from risk management to timekeeping for lawyers, counts Singapore"s Temasek and private equity firm Great Hill Partners as its investors.