From what I see below your sugnature, you car has survived 17 years and 176,000mi with a diet of mineral oil. Why would you think changing the diet of an old (mature) healthy combination.
Synthetic, by itself, will not necessary clean the inside of your engine. The cleaning action is not due to the oil being synthetic or mineral, but is related to the amount and type of the additive package contained in the oil. You can have a mineral oil with a very high concentration of detergent additives and an a synthetic oil with a very low concentratrion, and vice-versa.
If your engine has lasted for 176,000mi with mineral oil, you will not get very major differences going to synthetic. My advice would be to spend the same amount of money on oil, but change oil at shorter intervals.
If you intend to change synthetic oil at 5,000mi. interval, stick with mineral and change it at 3,000mi. It will cost you the same (approx) and your engine will be happier.