TV tie-in editions of the five extant Song of Ice and Fire novels were released alongside the first five seasons of HBO's Game of Thrones, with each new edition preceding the launch of the respective season by around a week, sometimes two or three. Other companies have been doing similar things, with Orbit Books launching TV tie-in editions of the first Wheel of Time novel two weeks before the TV show launched last November.
Similarly, tie-in editions of The Lord of the Rings are being issued in early July ahead of Amazon's Rings of Power television series, although in that case the gap is larger, at almost eight weeks.
House of the Dragon wrapped production last week and editing and post-production has been underway for some time. George RR Martin reported seeing rough cuts of the first few episodes several months ago, so five months to wrap post-production on the last few episodes seems reasonably achievable.
The new editions of Fire and Blood will hit shelves on 12 July, making the release of the TV show on 17, 24 or 31 July (HBO originals usually air on Sundays) fairly likely.