My daughter is 5' 2" and a TTR-125L is a bit small for her. That is what she learned on, but then I bought her a KX-100.
Keep in mind that the TTR-125 comes in two sizes. The small wheel version has a seat height of 30.5 while the big wheel version has a seat height of 31.7. By comparison, the KX-100 has a seat height of 34"
I would expect that at 5'8" tall your girlfriend would be tall for a TTR-125. It might be a good bike to learn on but if she starts trying to go fast a seat height that low is going to cause her a lot of difficulty. For one, it is difficult to stand up when your knees are in your chest sitting down. Second, the center of gravity gets way too high and can cause stability problems.
There are a number of bikes that have a seat height of 34 inches, which I would expect would be better for her. For simple trail rides a TTR-230 or a CRF230F would suit the bill. These have the advantage of electric start, which can be a great benefit for beginner riders.
If she is more aggressive then a CRF150RE might fit the bill. A 34 inch seat height, but it is MUCH lighter than the TTR-230 or CRF230F and even though it is lower displacement it is a high performance engine so in many situations it will out perform the mild mannered 230s
Rod