2.5 gallons of over 200 degree wort + 2.5 gallons of cold water = hot wort in my opinion.
You will still have to do a small ice bath.
Now that I'm on my 7th batch of beer in the future, a wort chiller is on my list BIG TIME. Back when I started with Mr Beer, it wasn't that important, because you boil the water, turn off the heat, and then add your ingredients which drop the temp, then mix that with cold water. Doing all grain and partial all grain, you are boiling a ton more water, which takes a LONG time in a ice bath, and a wort chiller is well worth it. You would probably even do a cheaper wort chiller and still put it in a small ice batch in the sink.