Could take up to 24hrs. I also think there may be a mandatory push at midnight with Verizon so maybe you are up and running this morning. You can either wait for the activation to occur or check your online account and when your new i5 is showing in your My Device then you are good to go! All the best with the new toy!
p.s. you should be able to connect to wifi and play around with it while waiting for activation. I know Verizon told me to keep my phone off by as I was fooling around with mine adjusting some settings, the notice that activation was complete popped up after about 2 hours. Definitely a nice surprise to get!