I have a phonetone cell phone repeater that uses a 6v ac adapter. The 6v ac adapter is malfunctioning. I connected a 5v ac adapter to the repeater and it works fine. Could this lower voltage damage the repeater or ac adapter?

5v ac adapter: Input 120 0.8A Output 5v 2.5A 12.5VA Max LPS
6v ac adapter: Input 120 1.0A Output 6v 2.5A 15.0VA Max LPS

 

Most of the times it won't.
Cannot tell for sure without checking the internal hardware of the repeater.
But if it works without generating heat it will be fine as far as I know.
The 5V adapter might generate more heat than the 6V as sometimes the lower voltage will increase the current draw. I have seen this in laptops when I repair them. I power them using a PSU and if I changed a 19V to 18V I can see the current increase. The laptop draws more current to keep the input power stable. Some might say a big NO to this but I a posting what I have witnessed with my own eyes.

 

I wouldn't worry about the lower voltage, but the lower power rating - 4W instead of 6W - is a concern. If its staying cool, it's probably fine.