Hi Edward. I didn’t really begin paying attention to my credit until a few years ago through a credit monitoring service. I came across an item from a collection agency that had been on my report since1998. Because I did not recognize the charge I disputed and they bureaus contacted the agency and verified that the amount was legitimate. I found out that it was an old hospital bill that I had forgotten about and it had been on report for almost a decade. I settled the amount because all they were asking for was $300 of the total amount due

In your situation, I would dispute the amount through the credit bureaus to determine if the info you’re being given is accurate. If you choose the settle, please know that while the collection status will go away, it may state on your report that the debt was settled for less than the full amount.

No you are not looking at this the right way at all. Debt never goes away even if they do not pursue it on your credit report. The consequences of not paying a collection agency is that they have the power to take you to Civil Court to collect the debt. You will then be under a Judge's order that is good for twenty years and can be renewed, The Judge at this point will also assess an interest rate to be applied to unpaid monies.
Now also you should not answer the collection agency if it is really old debt as they probably bought it in a bundle, unless they are working specifically for the card Company as a percentage case.. If you answer to their first letter it is an acknowledgement of the debt, even if you deny it. See if they send you follow-up letters, if they do then they probably have a pretty good read on the situation. At this point you can then ask them to verify all the purchases that constitute the total $5,000. Any purchase they can't verify you are not responsible for but be careful of your wording here when you speak to them. Or hire a Lawyer.
But by Law debt never goes away, even if it comes off your credit report.