With that leg length, traditional fitting philosophy would put you on 170s or 172.5s. After wide adoption of Cyrille Guimard's "long crank" fitting in the 1980s, cranks got longer. Greg LeMond, at 5'10" and with similar leg length, used 175s.

My inseam is a bit over 35". I started on 170s, as everybody else did back then. When longer cranks became widely available I switched to 175s and found my climbing improved, at the expense of my sprint.