Social Security: Best way to get Social Security?

My wife has started getting SS at 62. I am 61. My understanding is that the optimal thing for me to do it to sign up to get a spousal benefit when I am 65, and than get my own full benefit when I am 70. That way I get my maximum benefit, but I get something for 5 years before that.
In fact, I am told that I don't just get half of what my wife gets, but get half of her full retirement amount.

Is this correct? Any problems with this approach?