Page Templates

I now have another stupid question. I’m trying to edit/create a template for static Pages, but the thing isn’t taking. I’ve looked at the documentation on how to create a page template, and it simply says all I have to do is add these few lines to the top of the template I need to use:

<?php
/*
Template Name: Snarfer
*/
?>

Then name the file “snarfer.php”. Then, anytime the static Page of “snarfer” comes up, it’ll use the template defined (in this case, it’s the index page’s template – I just need the header text to change.)

But this isn’t working for me. I’m trying to create a static “links” page, and I have saved the files as “links.php” and put the template name (as seen above) as “links”. Shows up fine and is editable in the Admin area, but when I go to view the site, it’s still using the default “page.php” file.

Have I named the file incorrectly? I tried changing it (like with the category templates) to “page_id-5.php” (my links Page id is “5”) to see if that would take, but it was a no-go. Any ideas would be appreciated.