I just collected some information about attractions.Here they are:
| ATTRACTIONS | ADDRESS | ADMISSION | GETTING THERE |
80 Mandai Lake Road |
| Ang Mo Kio MRT(NS16)-Bus 138;Choa Chu Kang MRT(BP1/NS4)-Bus927 | |
2 Jurong Hill | / | Boon Lay MRT(EW27)-Bus 194/251 | |
/ | Sentosa Choice Package @S$33.90 | Sentosa Express(S$3/person/day) | |
30 Victoria Street | / | City Hall(EW13/NS25)-EXIT A | |
1 Esplanade Dr. | / | City Hall(EW13/NS25)-Underpass | |
/ | / | Outram Park (EW16/NE3);Chinatown (NE4) | |
Boon Tat Street | / | Raffles Place MRT(EW14/NS26)-Robinson Road | |
1 Beach Road | / | City Hall(EW13/NS25)-Beach Road | |
/ | / | Raffles Place MRT(EW14/NS26)-Singapore River | |
/ | / | Clarke Quay MRT(NE5) |
Actually more attractions are worth to have a look,even a long walk.So this is only a small part of my list.If you have any other idea or suggestion,please do not hesitate to tell me. 
Hmm i think these few places are more than enough. Do we have enough time to finish the above list in five days?
My friend recommend us to see dolphin show and water dance in sentosa, eat geylang tau fu fa and eat at restaurant beside trader hotel wor. Others in my list got Bugis Village, Suntech City, Orchard Road, Dicovery Science, Changi Village (see pondan wor, swt), Singapore Flyer, etc
Geylang there has a lot of hawker stalls and some of them are inexpensive and delicious.I think we will go there too.(P.S.That is a red light district too.)
Bugis Village is just neat Bugis MRT station and quite close to little india.Hence,we will go through these places in one off.
Suntec city is located near City Hall，as well as Singapore Flyer which may cost at lest S$30.Singapore Science Centre is 10 mins walk distance from Jurong East MRT.Tanah Merah MRT station is the closest one to Changi Village,and then taking Bus 2.
I will try my best to go more places.