Extend my wired Airport Extreme (5th Gen) with a 2nd Wired Airport Extreme (also 5th Gen)

With this set-up, will the strong Wi-Fi signal I now get in my house from the 1st Airport Extreme NOT be reduced?

That is correct, the wireless signal of the two AirPort would not interfere with each other and thus the signal strength at the house would not be affected.

And since the separate building is only 300 square feet, I assume the Wi-Fi signal there will also be as strong with the 2nd Airport Extreme being so close to everything?

Correct!

Could someone point me to SPECIFIC instructions on how to CORRECTLY set this up so that the 2nd Airport Extreme will EXTEND my home network?

You would want to configure both routers for a roaming network.

I wouldn't waste your money buying "special" cables, especially ones that offer gold connectors. Pre-made cables come in a variety of lenghts. Most common are 1', 2', 6', 10', 25', 50', & 75'. I would suggest at least two things: 1) Get either CAT-5e or CAT-6 cable, and 2) Use plenium-rated cables if you are snaking them through walls.

Since I already have the 1st Airport Extreme already connected & operating flawlessly, can I just hardwire & plug in the 2nd Airport Extreme in the 2nd location & proceed from there.

Question really is: I don't have to disconnect & unplug & reset the 1st Airport Extreme, do I?

That is correct, you shouldn't need to either disconnect or reset the 1st Extreme. It should just be a matter of connecting the 2nd Extreme, and then, configuring both for the roaming network. For the 1st Extreme that will be a minimal effort as all you need to do is verify the Network Name & Network Security type/password as you will need to use the same for the 2nd Extreme.

However, it is always good networking practice to power-down any networking or computing equipment when making physical changes to prevent electrical charges from damaging any of that equipment.

So, I should unplug the 1st Airport Extreme from the outlet before doing anything?

Yes.

Since the 2 Airport Extremes will be in 2 separate locations, which do I plug into the outlet first?

I would suggest plugging the one in the house first, then the second one in the backyard building. Be sure to connect the Ethernet coming from the first into the second before power-on either base station.

Could I connect the Ethernet both to the 2nd Airport Extreme & then to the desktop, then plug in the current Airport Extreme in the house, then run out & plug in the 2nd Airport Extreme in the separate building?

The key is to leave everything powered-off; connect the Ethernet cables, and then, start by powering up the house unit, then the backyard unit, and then, the PC. Make sense?

P.S. I have the Version 5.5.3 of Airport Utility for Windows (using Windows XP Professional with Service Pack 3)

There does NOT seem to be a later version than that.

That worked great for the installation of the 1st Airport Extreme several months ago, so I shouldn't have any problems, should I?

There is a later version (5.6.1) for Windows, but required Windows 7 to run on. Since you can already administer the 1st 5th gen Extreme with the version you have now, you shouldn't have any issues continuing to use it for the second unit.

No problem. Feel free to ask as many questions as you need to. I would only suggest that if you change topics it would behoove you to start a new post.

In this case, we're still on topic.

I have a short Ethernet Patch Cable left over from when my Internet Provider was Cox Cable.

But, it is only CAT5 (NOT 5e)

Would that be sufficient?

Yes.

What improvement (if any) could I expect using CAT 5e instead of the CAT5?

None as far as the maximum bandwidth of your current system is concerned. Once you start pushing past 1 GB Ethernet speeds, you will want to upgrade to CAT-5e or CAT-6 cabling. As long as these Cox-provided cables are in good physical condition, you should experience any performance issues using them ... and there are a number of utilities out there where you can make throughput measurements if you are concerned.