If you take half a 5-hour energy, do you stay really alert for 5 hours somewhat more alert for 10 to 15 hours?

Mileage may vary: As a dietary supplement, that product and it's claims are not tested or approved by the fda. So while it may very well make you more alert, there is no scientific data that i'm aware of that would show how strong the effects are, or how long they would last. As with any supplement, make sure you include it in the list of medications you report to your doctor if they ask.