Is There an Easy Way to Swap Pages?

You can just drag them around in the Pages panel. However, if you just drag the right page to a new position, the pages will reshuffle making the following left page fill the gap you just made. In order to prevent this, temporarilty uncheck "Allow Document Pages to Shuffle". Then drag one of the pages you want to move (e.g. p3) to the immediate right of the one you want to swap with (p.5) (note the darker black bar when you drag CLOSE to the edge of the desitnation page. You now have a 3 page spread. Now, drag the other page back to where the first one was, again dragging close to the edge so the black bar is darker. Turn "Allow Document Pages to Shuffle" back on.

Just watch for any objects that may have gone along for the ride from existing left hand pages.