For a ceiling fan, Hampton Bay ceiling fan Model# AC-552A. The diameter is 5 1/8", with the screw holes on the sides.
All of the mounting brackets I've found are 4".

If you can't find it at HD or Lowe's then I would think about buying a new fan.

You might also be able to get a whole new canopy kit; bracket, canopy and all.

Hampton Bay is a house brand name for fans made for Home Depot. They frequently have these in stock or you can order it from them.