My DC map of squares does not include squares numbered as high as 5578.However, from the high number, I'd guess it was beyond Anacostia.
Regarding Square 736 in southeast.It is bounded by 1st St to the west, 2d St to the east, E St to the north, and F St to the south.
Randle Highlands is bounded by Pennsylvania Avenue SE to the north; Naylor Road, 27th Street, and Texas Avenue to the south; Fort Stanton Park to the southeast; and Minnesota Avenue to the west.
Regarding Floral Hill, I found some old newspaper ads/articles describing it as follows:
1879:Dr. Lee White had a farm in Floral Hill.In the 1884 DC Directory, Dr. Lee White lived on Anacostia Rd.The farm was at least 15 acres and had fruit trees, grape arbors, berries, and all types of vegetables.
1887:An ad for cabbage plants and seeds for sale from W. Lee White's Sons of Floral Hill.In the 1887 directory, that business was located on Anacostia Road.
1891:"One of the row of trees in front of Dr. W. Lee White's place, Floral Hill, was destroyed, blocking the roadway and demolishing part of the recently erected electric bicycle railway."
1893:dangerous "open man holes on Minnesota Avenue in Floral Hill."
1902:a request that "trees be planted in the vicinity of Floral Hill on Minnesota Avenue and 28th St."
Check your email.I've sent you some maps showing the general locations of Randle Highlands and Floral Hill.