Then go 1 step at a time
I don't think your outline is complete so I'll go 1 point at a time.
1) Pretty straight-forward, nothing to add here.
2) What does "steadily" increasing mean exactly? You increase the number by the number of minutes left between current time and 5:30 or what? What's the rule? You cannot tell the computer to "steadily" increase the numbers because computer doesn't know what steadily is. You need some sort of interval here, based on either second / minute / hour / some other measurement unit valid for the given interval.
3) Now this is a tricky one. You only have 5 integers to work with, unless you wanted to include floating point numbers.
You are assuming that there's a single point of failure here - seeing number 5 and then seeing number 4, which implies user connects twice.
But the user might connect.. 1000 times during that time period.
You also need a way of tracking the user - either a login system (OpenID, Facebook one or your custom one) or you can attempt to track them by IP - either way, your logic imposes a certain way of being able to track the user.
Once that system is in place, you can employ the logic on how to track numbers they saw.
As you can see, there's quite a few variables here, until you clear them up - no way to move on