Are you sure you really need to run the app at 5AM on a timer? Why not just run it when you wake up in the morning? By the time you leave the house, it will surely be downloaded.
Most newspaper apps download the news to a local cache, and so you can read the news even if you are off-line. (Hopefully, it doesn't give you annoying popups about not having a connection!)
Typically, they don't take much time to download - even if you have a slow Internet connection, I can't see it taking more than 1-2 minutes to do the download. But even if it were to take 15-30 minutes (which would be outrageous) it would be done by the time you leave.
But, no, right now on iPad, there is no way to run an app at a certain time. that might be possible in some future version of iOS 4.x, but currently isn't supported. Under iOS 4.0, it MIGHT be possible for somebody to write a newspaper app that would do that internally. (Depends on how Apple interprets their rules on what apps can/can not do in background.)
But given that newspapers take so little time to download, I don't see the point.