HP is suing Mr Lynch, and Autonomy's former finance chief, following the US computer  giant's Â£11bn takeover of the business in 2011.
The US firm alleges "accounting misrepresentations" led HP to massively over-pay for Autonomy.
But in a filing in London's High Court, Mr Lynch blamed HP "incompetence".
He denied wrongdoing, and accused HP of making statements that were damaging to him and misleading to the stock market.
HP's takeover of Autonomy was a major strategic move for the US company, designed to take it into software.
But HP eventually wrote off three-quarters of the company's value, and accused Mr Lynch and finance head Sushovan Hussain of mismanagement. Both men strongly reject the claims.
In interviews on Thursday with Reuters and the Financial Times, Mr Lynch claimed that documents would show HP's handling of Autonomy after the takeover was "incompetent".
He said divisions within HP were "at war" with each other.
HP said Mr Lynch's lawsuit was a "laughable and desperate" attempt to divert attention from its own $5bn claim and that it "anxiously looks forward to the day Mr Lynch and Mr Hussain will be forced to answer for their actions in court".
Mike Lynch, founder of UK technology firm Autonomy, has hit back at Hewlett-Packard with a $150m (Â£100m) counter-claim in their long-running dispute.