Do you consider your child advanced, or "gifted"?

DS is turning 5 in a few weeks and we are in pre-k. He can read since 3 years old. At 5 he can read quite fluently, spell simple things, and was doing crossword puzzles. He is also very interested in math, and can do simple addition and subtraction.

I never really think too much about it until another mom from our class called me out of the blue. She told me how our teacher told her that her DD and my DS are more "advanced" in class. She is a bit concerned that her DD is not challenged enough in our current class, and she wonder if I felt the same. She has visited another school for gifted children (in order to be accepted you have to take your child for a test to see if they are "gifted"), and she asked me about my thoughts and how /if we should talk to our school about it.

For the past few weeks, DS has been asking me what is the meaning of "a plot", "to inform", "persuade" mean, which he probably read somewhere via the ipad app our school gave to him for extra reading. I thought they are pretty complex concepts for an almost 5 year old. This made me think if I do need to help and push him more? I just don't know what else I can do.

Do you think you have a gifted child, what makes you think so, and what do you do with him/her? Do you take them to tests, and enroll them in special programs/schools for the gifted? Any other ideas? What is your viewpoint on this?