I am looking for the font for the words "high country" and "bank".

Thanks!

Eurostile Extended Bold  Suggeriti da Brown013 
Times New Roman  Suggeriti da Brown013 

High Country: Times New Roman

Bank: Eurostile Bold Extended

The top of the h, n, and r don't quite match so I'm not so sure that it's Time new roman.

They match perfectly.

It was easier to tell in your original post (the one that was deleted). Which was why I had suggested a modified version of Times New Roman. Obviously the g doesn't match, but everything else does.

Your earlier comment jerseygirl was, imho, correct. With this one I disagree. That the 'g' has been played with is clear so, 'modified'.
But, the rest does not perfectly match with the Times New Roman. Try this, superimpose the times New Roman 'g' and 'o' on the sample and look at the top of both. Though differences are minimal with other letters, like the 'h', 'u' and 't', it is just a bit off.

There are of course a great number of Times New Roman copies out there and one of those may be the perfect fit but with this image it is hard to tell.

Thanks!