The 10 000/13 000 miles service period is making service more economical than more frequent service periods would do, still almost twice as frequent as that for European cars (2 years/about 19 000 miles). This shows that modern engine oil can easily handle the official US service period, the Euro one and actually more.
Your cars and you can do what you want but I would save the money for some other maintenance for the car.
I'm no oil expert but those who are explain that oil additives are built to activate only once the engine oil reaches running temperatures. It takes some time before all get full power. This means that the engine faces additional wear first from the fact that you run it with low oil for a short while after the oil change (before the filter and pipes get filled up) but more importantly the oil performance is initially lower than say after 1000 miles. 5000 miles service period should not be harmful but nothing better than 10 000 miles (assume normal driving, not just very short trips). A bit useless to discuss this because those who change oil every 3000 miles have a firm opinion from dino oil experience and nothing can change their mind.
Although it may be useless to discuss this, I will since this is a forum and created for just that, discussion.
There is no way your going to convince me that changing the oil more frequently can cause any harm. On initial start up, after an oil change you should reach proper oil pressure within a matter of seconds and reach oil temp in just a few miles depending on driving style and outside temps.
I've been using full synthetic oil in high performance engines for many years and the one thing I have learned is that the lubrication properties of these oils are so good compaired to conventional oil that we would usually use conventional oil durring a break in period because the synthetic would not allow for propper ring seating. But, that's not to say that they will not break down. If you compare (synth) oil that has been run in a motor for 4-5k miles to oil that has been run 10-13k miles. I will guarantee that there will be a big difference in viscosity break down.
All this being said, I just like to work on my cars and will change my own oil twice as often then the dealers recomended intervals for much less money and more peace of mind.
But I guess time will tell if there is truely a benefit.