Oil Change Question

No, it shouldn't. Esp if you're going to continue 5k mile intervals. Even dino oil should hold up for that long with no problems whatsoever.

 

You could probably add the synthetic oil to your Jiffy Lube freebies for the cost of the oil.

And for what its worth, I'd never let Jiffy Lube touch my car. Far too many horror stories from others - including the case where they didn't replace the drain plug.

 

I don't think that the dino oil will hurt the motor at all.
Your motor is 12 years old.
If it's not using oil and you're changing your oil every 5k miles then you're probably not going to have any oil related problems with the motor now or ever.

There are people that say that if you use this filter or you don't use this or that designer blend of synth-o-oil then your motor will explode.
I've used Castrol 5w30 for years and I've also used Fram filters since I can get both in any city or town that I happen to be in at the time. I've never had any oil related problem with any motorcycle, car, tractor, or other ICE that I've owned, and more often than not I put WAY over 100,000 miles on a car before I even think about getting rid of it.
The main thing is that filters and fluids need to be checked and changed, and you do have to use fluids specified by the people who built your car.
Many owners trade their cars out every 3 years or so or never see 200,000 on their odometers, and so their "expert advice" is often based on second or third hand information since almost ANY ICE will get to 100,000 miles even if you skip a few oil changes.
This is especially true in the motorcycle community where it's a very rare rider indeed who will put 100,000 miles on a bike or bikes.

Change your oil.
IIRC, for a G1 the 5w30 will be fine with a 5K interval.
Check the dipstick at least semi-occasionally, and investigate any volume loss and monitor your fuel efficiency.

You'll be fine.