It would be interesting to know how those pages function in IE5. Does anything they do rely on JS IE5 doesn't understand? CSS IE5 can't process? eBay, Amazon, and Facebook especially might become worthless even though it looks like they render in a usable fashion.
Although I am not certain about it, the way browsers are expected to handle encryption may have also changed in 14 years -- making payment gateways on these websites wither unusable or risky.