First of all, you should check your pocket before deciding to visit New York because it all depends on your budget. You budget will help you to determine which type of activities you can do and enjoy in New York.
You can visit all monumental places of New York and can also enjoy many memorable things in just five days if you have a lot of money. But if you have a limited amount, then you have to be very careful in making selection of places where you want to go in New York.
You should do a thorough online research to know the places where you should go in New York. You will find numerous websites revealing the attractions of New York and it will be easy to decide where you should go according to your budget.
You can also visit NYCgo.com for getting information of sightseeing in New York and this website will also help you in planning your tour in an organised way. You can also decide which places are best and easy to access through the city map on this website.
You should make a complete plan of how you can visit all these places in five days. Try to divide your and visit the nearest areas first. Then visit those areas situated on longer distance from your hotel.
You need to plan in a way that your each day covers all major attractions of one particular area of the city which will help you to visit all major parts of the city in five days.
Make sure you do not miss your visit to the Staten Island Ferry, Wall Street, Museum of Modern Art, Empire Star Building, and Statue of Liberty as these are the most visited attractions of New York.