Should I change oil when the computer shows change oil soon or do it at a regualr interval of 5000 miles?

Assuming this is an oil life monitoring system and not just a light that goes off based on mileage, follow the oil life monitoring system. It may work out to your advantage, because oil wears out based on usage...if you are easy on your oil, it will last you much longer than someone who is hard on their oil because of driving habits and conditions.

The manufacturer spent millions developing these systems, use them. There is NO advantage to ignoring them.

Modern engines have a way of logging the engine load over time and calculate the so-called variable servicing intervals which are then displayed on the dash as a reminder. This approach is largely supported by the recent breakthroughs in modern synthetic lubricants and built-in long-life additives.

If the typical car usage is a normal one, you can stick with the variable intervals, but making sure you use premium long-life synthetics both at engine oil change and for topping up. Otherwise, you may opt for a fixed service interval and slightly more modest (and cheaper) oils. In terms of costs, it will come out about the same - expensive oil and longer average intervals vs. cheaper oil and shorter intervals.

Why use synthetic and change it every 5K? You could use conventional.