sync button on 5 year old xbox system

The button on the left side of the system is the sync button you have to press and old it for like 5 sec then do the same for the controller sync button thats on the top of the controller. Hope thta helps.

The microphone would sync the same way as on the old xbox's. The sync button is found on the front of the console just to the left of the usb ports. Push it and then hold the power button on the microphone for about 4-5 seconds. This will sync the mic
up for you.

Tried all of those options, including holding the sync button down, with it horizontally and vertically, and same results each time. It's an older system, at least 4 years old now, so the warranty is long expired. Am I stuck at this point with getting
a new system?

You could just try to reset it via troubleshooting menu:

So, let's try this:

If your console is a digital version, try this way:

1. Turn off your Xbox completely by holding the power button for 10 seconds.

2. Press and hold the Sync button.

3. Press the power button, and keep holding the Sync button.

4. Keep holding the Sync button, until the troubleshooting menu appears.

5. Select the option "restore this xbox" and choose keep my games and apps.

If your console is not a digital version (Has the disc reader)

1. Turn off your Xbox completely by holding the power button for 10 seconds.

2. Press and hold the Sync and Eject buttons.

3. Press the power button, and keep holding the Sync and Eject buttons together.

4. Keep holding the Sync and Eject buttons, until the troubleshooting menu appears.

5. Select the option "restore this xbox" and choose keep my games and apps.

And also, Try to offline update the console like these:

https://support.xbox.com/en-US/help/hardware-ne...

In the link above go to the tab: "Download OSU1 System Offline Update File"

If your console is the Original Xbox One:

Important! For Build 6.2.9781.0, use the OSU3 Offline System Update file. For all other builds, use the OSU2 file.

Go to the tab: "Download offline update file from OSU2 or OSU3 system"

the wired controllers i have don't have sync buttons. i'm wondering if the problem is that i am using brand new black controllers on a four year old white xbox? are the black controllers designed for the newer xbox slim?