Yes, you'll want to add CYA prior to adding bleach to protect it from the sun. Otherwise it will burn off from the UV before it is effective. How much do you have. I buy it at Menards (home improvement store) for fairly inexpensive. I know that is relative, but certainly makes sense to try to use what you have to minimize costs, especially it that means you'll be able to purchase the test kit.
And just to reiterate, if you drained and refilled the only CYA present will be what you added. If you added none, you have none. Pool Math is very convenient for estimating ppm's - use the "effects of adding chemicals" at the bottom to estimate what the effects will be of what you have on hand and see where that gets you. Just be sure to change the pool volume at the top left of the page to 5600 gallons.