Unless you filled out a play slip for more than one draw, or asked the clerk for more than one draw, no. The 5 rows just means that’s 5 different sets of numbers to match up against the winning numbers. I’m not sure where it would say it on the CA slip, but when you play draw games for more than one draw in Georgia, it will say the dates that the ticket is valid for, just above the draw numbers.
You will definitely have to buy another ticket for the next draw.
Welcome to playing the lottery! And good luck!
Edit: just for more info