Ammonium Nitrate is 34-0-0, and it does not have any sulfur in it.  So, it can't be Ammonium Nitrate.

I figured it is a blend of urea, and Ammonium Sulfate.

If you use 21 lbs of Ammonium Sulfate, you would get the 5 lbs of Sulfur.  Then it is a matter of adding urea to get the 35 lbs of nitrogen.  You would need to add 66.5 lbs urea to get you to 35 lbs N.  ESN is 44% N. If you blend in 69.5 lbs of ESN with the 21 lbs AMS, you would get to 35 lbs Nitrogen.  Of course, you would have to blend in some filler to get to 100 lbs.  Not sure who does that anymore, so I don't know what materials are being used to get to 35-0-0-5.  If you do a blend of 60% urea, and 40% Ammonium Sulfate, you should be able to get 36-0-0-9.6(sulfur) - twice as much sulfur as the O.P. said.

My concern with the urea is that it doesn't have sulfur in it. Based on soil tests results that I see, I think adding some sulfur is important. Unless the O.P. is adding sulfur in another way, I would look at going the 35-0-0 route.