That is a good question.
The ES175 has a 16 inch lower bout.
The AF105NT that I had...the new Artcore Custom models...had a 15.50 lower bout, and was also shorter in length by about an inch.
You can usually squeeze a guitar by 1/4 inch all around into a case, compressing the padding, but I don't like to do that.
I did a case switch with my FA100 and my AF105NT...and the AF105NT fit fine in the original FA100 Ibanez case...but I don't remember if the FA100 fit into the grey AF105NT case...if it did, it was a tight fit especially in the headstock area due to the guitar being bigger than the AF105NT. The FA100 has the same size as the ES175....16 inch lower bout.
Take a look at the TKL cases and their copies....they have the standard sizes that fit ES175, ES335 etc...
http://www.tkl.com/?siteid=search&qsearch=small%20jumbo&sh=Guitar%20-%20Small%20JumboAlso, why not take your HR to a music store, and to some case fitting...they usually carry most sizes...and if you don't like the price...make a note of the model, and try getting it cheaper online.
The size you need for an ES-175 is the same as for any dreadnought.
So you need a dreadnought case with an arched lid.
I use an Ibanez Lonestar case for my Epiphone Zephyr Regent (ES-165).
(I bought that one before my 2355M). But I could also use a Guild case.
The ES-175, the ES-165 Herb Ellis and the Howard Roberts are all the same size, there's just some variation in pickups and soundholes.
Golden Gate is a nice brand for cases. I know that an Epiphone Howard Roberts fitted well in my Golden Gate case. I just don't know what type number it is. Could be C-1510, but I'm not sure. Better call first before you order anything.
Ginger