As Fiddlerman pointed out, arm length is a key factor. At your height, your arm length is mostly likely in the full size violin range, but everyone is different. Measure your arm and see which category you fall in. If your measurements are borderline between two categories, see if you can try out the two sizes.

Finger length will also make a difference. I'm not sure where you are in terms of learning violin, but I found that the violin size really started making a difference when I started using 4th finger. I am a short adult who started in a full size but switched after a few months to a 7/8. The smaller size works much better for me.

Sound quality will generally be better with larger violins, so you will want to use the larger size if your arms and fingers are long enough to allow it.