For a bake sale, Dora makes 203 cookies and places them in two bags. Each bag holds five cookies. Dora fills as many bags as she can and saves the cookies that remain. How many cookies does she say?

Dora has 203 cookies and each bag holds 5 cookies, so she can fill 203/5 = <<203/5=40.6>>40.6 bags.

She can fill a total of 40*5 = <<40*5=200>>200 cookies in the bags.
So, she saves 203-200 = <<203-200=3>>3 cookies. Answer: \boxed{3}.