Hello,
Someone I know told me this was a good place to get some helpful advice in learning to use my new camera. I have been studying my manual. It seems like the more I read, the more questions I have.

I have a T5i and a the lens that comes with it. I am excited to get started taking some pictures, but I am not sure which mode to choose. My kids told me if I turn it to auto, it will be exactly like using the little camera I have now. I was hoping for more than that when I got this one. Which mode would be best for a beginner?

I have bought a ton of things, including camera gear on eBay and never had a problem, just do the homework, check the rating, check the reviews for similar type items. Everyone is different related to their tolerance regarding rating, some will only buy from those with a 100% rating. I get that but if the person/business has only sold 7 items that's one thing. I personally will buy from someone/place that has a 99% rating if they have sold a large number of items, say 1000+. It can be difficult to maintain a 100% rating because you always run into someone that expects the used item that is 50 years old to be in perfect shape even though you describe it as 'used with normal wear and tear.' But just like normal purchasing, if it sounds to good....

Guide numbers may be calculated by multiplying the f stop x distance. (shutter speed and duration are not part of the calculation).

Some LED lights are sold with GN as part of the specification (B&H quote GN on some of their lists) http://www.bhphotovideo.com/c/buy/Macro-Ringlights/ci/649/N/4168864821

Most LED lamp manufacturers do not quote GN for the simple reason they do not remain constant on battery power. I have four 128 x bulb arrays, all made by the same manufacturer, all the same model, but all with differing power output. These are battery powered without close tolerance voltage regulators and as the voltage from the battery packs go down, so does the light output and ipso facto, so does the guide number.

When the batteries are fresh, my LED lamps have a GN of about 10 (using feet as the distance measure and at ISO 200) and after an hour of continuous use this GN diminishes to about 5 or 6. I would add that these units are of the cheap and cheerful variety as opposed to those higher quality products used in professional studios.

A really good (understandable) article which explains GN and includes an exposure calculator can be found at http://www.scantips.com/lights/flashbasics1c.html

Edit: Two more reasons for not quoting GN on LED panels:
The panels are dimmable (everchanging GN)
The colour temperature on some units is adjustable and therefore the GN is not constant.