New to email lists, looking for guidance

I've never given much thought about creating or maintaining an email list until recently. The emails are automatically stored in my database when a sale is made. I have a list of around 5,000 names in a specific niche as they were all customers who purchased a service from one of my sites, but I don't know anything at all about the legalities of sending emails to these people promoting another product. I have a privacy policy in place that mentions emails and other info is collected if they choose to make a purchase, but it doesn't mention anything about me sending them emails. To be honest, I just copy/pasted the privacy policy from a similar site a few years back when I set up the site. Would this be considered "opt-in"? I mean, the privacy policy doesn't specifically say "hey, I plan on sending you emails with some similar

So, if a customer buys something from me, do I have the right to send them emails since they willingly supplied their info and agreed to the privacy policy when signing up? I was thinking about sending them an email using a template for a clickbank product I am starting to promote, as it's in the same niche. Is this a good idea? I really have no clue about sending emails like this as I have never done it, and don't want to make any rookie mistakes. Advice/suggestions?