You couldn't go if you wanted too on such short notice. You need to make reservations in advance, and they sell out.
If you go on their web site, and act like you're going to book a vacation, a calendar will come up with the available days. Don't worry, it asks for the credit card at the end, and they won't hassle you after you enter your e-mail address. They're usually sold out 1 month into the future, sometimes even 2 months.
A 5 year old is kinda young for DC. At that age they won't really understand how big of a deal it is to visit this park, and they can't go for the dolphin swim and the water will be cold to them. Whereas my 10 year old daughter is the one who wanted to go after feeding the dolphins at SWF. She knew this was a big deal to go, and appreciated it. And after we got into the water, she didn't care about it being cold.
Yes, save your money and wait.