To help explain OP's interest, every Presidential Inauguration since George HW Bush's has featured five US flags behind the dias. The outer two have been the Betsy Ross 13 star flag, the middle has been the current 50 star design, and the two flags flanking the middle have been the US flag that was the official flag when the incoming president's home state was first admitted to the Union. Bill Clinton's was the 25 star flag for Arkansas's admission, George W Bush's was the 28 star flag for Texas's admission. Barack Obama had the 21 stars for Illinois, and Donald Trump had the official 13 star flag since New York was one of the original 13 states.

Prior to George HW Bush, Reagan's first inaugural featured the 50 star flag on one side, the Betsy Ross on the other side and five red white and blue banners.

So why was HW's the 38 star flag? That would represent Colorado in the current scheme which HW had no real ties to. Did somebody goof and pull the 38 star flag instead of the 28 stars for Bush's Texas?

EDIT: Bush’s inauguration was the bicentennial of Washington’s in 1789. The 38 star flag was the national flag for the centennial in 1889 for Benjamin Harrison’s.

Thanks to /u/silverappleyard for the idea.