Help! How do I reach my goal?

Hello everyone! I am currently at 172 (32" waist) and I am 5' 10". My goal is to get down to 150 and a 28" waist.

If I weight train 5 days a week along with an hour of cardio 3-4 days a week, will I get to my goal in 5 months? (By May 22nd)

I have no idea how to calculate any of this...like how much I need to lose a week and stuff so if you guys could help me that'd be great!

Note: My BMR is 1,600 and I'm eating 1,750.