Edward S. Lampert is hoping the third time’s the charm in his bid for bankrupt Sears Holdings Corp.

The updated ESL Investments’ bid for Sears at over $5 billion includes additional amounts to pay administrative claims and another 57 real estate properties.

Sears made a non-binding offer of $4.6 billion on Dec. 6, followed by a binding offer of $4.4 billion on Dec. 28, which was met with contentious debate from creditors concerned about Sears heading toward an administrative insolvency. The updated bid incorporates the terms of the $4.4 billion bid, including a $1.3 billion credit bid, plus new terms.

The bid was made by ESL affiliate Transform Holdco. And the letter from Transform to Sears’ financial adviser at Lazard Frères & Co. also reconfirms a valuation of $35 million as the settlement for a release that Lampert sought to bar the possibility of future claims against Lampert and ESL over past transactions between the retailer and the hedge fund. The unsecured creditors committee in the Sears bankruptcy wanted to do a deeper dive on the past deals over conflict of interest claims. Lampert is chairman of Sears and ESL, and is also chief executive officer of Transform Holdco.

The letter dated Jan. 9 states that it details the terms agreed to by the parties at a bankruptcy court hearing on Thursday, and therefore has “qualified bid” status.

ESL said Thursday it “is pleased to confirm the submission by the deadline of a significantly improved going concern bid by Transform Holdco LLC, a wholly owned affiliate, for substantially all of the assets of Sears Holdings Corp. for a total consideration in excess of $5 billion, as well as the requisite deposit of $120 million.”

ESL emphasized that it believes its proposal “will provide substantially more value to stakeholders than any other option, in particular liquidation, and is the best path forward for Sears, its associates and the communities….”

A bankruptcy court-approved auction is scheduled for Monday.

As for terms of the new proposal, it includes an assumption of up to an additional $663 million in liabilities. The components include additional payments for goods ordered by the company before the deal closes and other costs, such as for severance and property taxes. One key addition is the amount of up to $139 million in administrative priority claims. That was a key battle point of the creditor constituency groups who argued that the $4.4 billion bid wouldn’t be enough to pay administrative costs connected to the bankruptcy.

The upped purchased price also includes additional assets that were slated to be left on the table, including accounts receivables, certain inventory, as well as the purchase of an addition 57 real estate properties.

Financing isn’t a problem as the letter details additional financing commitments, as well as the additional deposit of $120 million that was required. Transform Holdco also said it agrees to be the back-up bidder in case a better offer is selected, but for whatever reason the winning bid can’t be completed.

Shares of Sears Holdings, which now trades in the over-the-counter exchange, on Thursday closed up 20.6 percent to 48 cents on confirmation that ESL has a new “qualified bid” on the table.

Sears filed its Chapter 11 petition for bankruptcy court protection on Oct. 15. The company operates over 500 stores under the nameplates Sears and Kmart. Lampert, if the updated bid succeeds, can claim he bailed Sears out of bankruptcy, like he did with Kmart Corp. in 2003. A year after Kmart exited bankruptcy court proceedings as Kmart Holding Corp., he disclosed Kmart would acquire Sears, Roebuck & Co. The deal, which was expected to create a retail entity doing annual volume of $55 billion, closed in 2005.

Sears had about 68,000 employees at the time of the bankruptcy filing, and ESL has said that buying Sears, instead of liquidating the operation, would save 50,000 jobs.