I am 176cm (>5'9" for the SI challenged) and one of my ex-partner was 164cm(5'4"). We had the problem Jonathan described towards the end of his message for the first year. After that we managed the difference really well and competed successfully and reached the open (5 dance level.) She is dancing now with a guy taller than me.
I think however that not the full height is the most important thing but the length of the legs. So if your partner happens to have longer than average legs the might help. The arm hold will be no (big) problem if you can move your center together.
I warn you though: there is a danger in starting assessing your partner and your bodytype to see how you fit, and further noticing flaws (arm, leg, neck length etc). It is not healthy for a romantic relationship in case you happen to have that with your partner.
[start offtopic rant]
Since I dance, I noticed that I am bow legged, my spin is curved to the side in my upper back, my head is poked forward, that I cannot fully extend my leg (that is not to 180 degrees but only to say 175) my hair is unfit for the competition hair style. And my partner once said that my butt looks big, and I tell you that it is smaller than the slimmest 10% of the population has.
To be honest I fixed my poked head and improved my leg straightness (which mainly comes from muscle tightness), and I noticed that my butt (which is just muscle) looks smaller if I stretch well.
[end offtopic rant]
Good luck with your partner,
Matyas