Answer
An average eye blinks 720 times per hour, 11520 times in a 16 hour day and 4204800 (365 days) or 4216320 (366 days) times in a year.
Work Step by Step
One minute has 60 seconds so an hour has 60 * 60 = 3600 seconds
blinking every five seconds means that you blink $3600\div 5 =720$ times per hour.
In 16 hours you blink $16* 720 = 11520$ times.
One year has 365/366 days, which means that you are 16 * 365/366 =5840/5856 hours awake. In this time you blink $5840/5856 * 720=4204800/4216320$ times.