You can add
Meta refresh tag to your page[
^]
And on Page_Load do whatever you have to do.
The major problem is that the page HAS TO BE OPENED IN THE BROWSER. So, either you have the page on the server opened constantly or you have to open it somewhere.
Alternatively, you could create windows service ON YOUR OWN COMPUTER or any other that you DO have access to, that would call your page every 5 minutes via WebRequest. But then that computer should be online 24/7.
Using web only is senseless requirement. The technology is not built for this and you should really describe your problem in more details and let us help you.
WHY are your options so limited? What do you have to do?
If this is something for your site which you're hosting and have no access to anything but web technology...how about database? There are scheduled tasks that you can program to do whatever. Today database servers are capable of running .NET code, send e-mails and gazillion other things.