You should first get your site off of Goddady, I would recommend Nexess. They have a hosting account for as little as $20 month
second, you should upgrade. But how to do it is a big question and can't be answered here. You should hire someone to do it for you if you are asking.
From 1.5->1.9 you will have quite a few theme and module modificiations. You should be aware of this.
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