How do I make a "title window" appear in a REALbasic program, so that
it pops up as the program launches, waits five seconds (via the timer
tool) and closes, followed by the main window of the program?

You should probably make the "Title" window the main window, which
will have a timer that will wait 5 seconds, open your "real" main
window, and close the title window.

Indeed, you should make the title window as the main window.  To
change it as such, go to Edit/Project Settings and select it from the
Default Window popup menu.  Now, in the title window, create a timer,
setting its mode to Single and its time in milleseconds to how long
you want the window to stay up.  In the timer's action event, put the
following code:

mainWindow.show
titleWindow.hide

I've tested it, and it works without a hitch!

Beautiful, you guys! Thanks!