The heights of 4 athletes on a team are 135 \mathrm{~cm}, 160 \mathrm{~cm}, 170 \mathrm{~cm}, and 175 \mathrm{~cm}. Laurissa joins the team. On the new team of 5 athletes, the mode height of the players is equal to the median height which is equal to the mean (average) height. How tall is Laurissa?
Answer Choices
A. 135 \mathrm{~cm}
B. 160 \mathrm{~cm}
C. 170 \mathrm{~cm}
D. 175 \mathrm{~cm}
E. 148 \mathrm{~cm}