I Weigh 184 And Am 5 Ft.5. How Many Calories A Day And Exercise To Lose 50 Pounds In A Year?

That is a very hard question to answer.
Are you looking to just lose 50lbs of fat, or whatever works the "best" to get to your desired weight goal?
Mind you that muscle weighs more than fat.
Because i don't know what your REAL goal is, i'm going to shoot a random program for you that could help you lose the weight only.

I recommend taking in an average of 1800 calories daily.  Exercise 5 days/week.  

Resistance training -
alternate body parts daily.
Ie:  Monday - chest and tricep workouts/Tuesday - bicep workouts/Wednesday - leg workouts/Thursday - shoulders/Friday - abdominals

Cardio training-
MUST also be incorporated.  At least 3 times a week.  I suggest running, because running burns the most calories.  Swimming is also another good alternative.

Q: Why is it essential to incorporate both resistance and cardio training?
A: Resistance training aids in greater overall strength, faster metabolism, you looking and feeling your best.
Cardio training helps burn more calories, gives you better sleep, and improves your cardiovascular system.

The "solution" to your question only provides general information on working out.  Should you require an answer containing more detail, do not follow any of the advice provided above.

Simple answer... For each lb you wish to lose you must burn 3500 calories more than you take in. Therefore if you want to lose 50 lbs in a year, then you need to lose a little less than a lb a week. Lets go ahead and say a lb a week to make it easy though. If you consume 1800 cal/day then you would be consuming 12,600 calories/week. So you would need to burn 161,000 calories total to lose that one lb. Just being alive will burn some of those calories for you. But for your ht/wt 1 hour of continuous housework will burn about 290 calories. So it would take you about 56 hours of housework to burn off 1 lb. Low impact aerobics would burn about 417 lbs so that would take you about 38 hours of exercise. So you see, it depends upon your current fitness level and what you take in as far as calories. I wouldn't suggest you take in less than 1800 cal/day though because if you do your body may take that as you are going through a famine period, and will hang on to your stored fat and you may lose muscle mass. This is why starvation/anorexia never works out well, plus you need that food for energy to continue your exercises. Good Luck, Susanne