If I understand you correctly, you want to KEEP your current LIVE store running while you build a new 1.5.0 store, right?
The SMARTEST way to do that is this:
a) keep your live store running, as-is. With its own admin. Own database. Own folder of files on the server. Everything as-is.
b) build your new store. THIS IS ONLY FOR TESTING AND PREPARING FOR LIVE DEPLOYMENT.
But, when it comes time to "go live", your temporary "new" store will be out-of-date because you'll have new customers, new orders, new payments, new products, etc in the live store.
So, simply upgrade your live shop (since it has the most current data) (THIS IS AFTER YOU'VE BUILT AND TESTED YOUR "TEST" 1.5.0 SITE IN PREPARATION):
a) put your live shop down for maintenance
b) backup your live database for safekeeping
c) replace all the php files/folders/images/everything with the new files (except the configure.php files which stay the same)
d) run zc_install and choose database-upgrade
e) re-do any admin settings relevant to the new setup (since you took notes while you did any additional customizing in your temporary 1.5 site)
f) turn off down-for-maintenance
g) do a test transaction to be sure checkout works
h) Do another backup of everything for peace-of-mind.
Take a deep breath.
You can then delete your temporary 1.5.0 site (files and database) because it's no longer needed. It was only ever used for "staging" to prepare yourself for the actual live upgrade of the live shop.
ADDENDUM:
If you are considering changing webservers or hosting companies, do ALL of your upgrade activities BEFORE or AFTER the move. NOT DURING. You want to make sure the site is working correctly before moving to another server, and if you confuse the picture by doing an upgrade at the same time, then you make it nearly impossible to determine whether your problems are the result of "moving" or a result of errors in "upgrading". So, always upgrade before OR after, but never "during" a move.
More about moving to another server here: http://www.zen-cart.com/content.php?142-i-want-to-move-my-zen-cart-installation-to-another-host-or-a-different-server
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