Grydan said:
Come up with a compelling argument that will convince WotC corporate, their corporate parents at Hasbro, Hasbro's shareholders, and the lawyers that the OGL (or something like it, tailored to 5th) is good for them.
Grow The Hobby: "Free to play," and then selling books and adventures, helps expose your game to the widest possible audience.
Discourage Piracy: If the core rules are available for free, fewer people will download the books "just to check out the product."
Maintain Current Market Presence Without Creating Product: Let the upstarts work to advocate your product for you by making things that you never would, or generating products in slow periods. All the cost of developing new things you've effectively put on the shoulders of those willing to shoulder that cost.
Dissolve the Major Competitor's Advantage:
Pathfinder's OGL game keeps them well-regarded, sympathetic, and agile. If you DON'T go OGL, you'll still have to compete with the OGL.
Make the Game Own-able: The biggest spenders on your game are the trufans who dedicate significant portions of their lives to it. Anything that can create a sense of ownership in the player base is to be encouraged, as that digs the brand deep withing the person's life, such that brand loyalty can dig deep. Allowing amateurs to publish their own works for others to get cements that loyalty like few other things.
Recognize the Reality of Your IP: D&D has always been a game built on the intellectual property of others. Without the proprietary works of creators like Tolkein, Howard, Leiber, et al, and the public domain that these authors in turn used, there would be no D&D. Additionally, as a game, many of D&D's innovations cannot be considered the property of their "creators" (more like "discoverers," but eh). The OGL recognizes this, and leverages it to advantage, rather than trying to erect a wall around it.
...is six reasons enough? I can probably do more.