Well I can't comment on your present circumstances, but if you are even considering coming to work out of Singapore (particularly with a family) for US$3000 a month then you must be in pretty desperate straights at the moment.
Let me expand. Accommodation has come down some 20% in the past few years, but anything vaguely decent in furnished rental accommodation, as opposed to sharing a loo and a kitchen type arrangement is going to be a minimum of 2500-3000 S$ / month. Then you have the water and electricity and loo tax etc. Expect at least 200+ S$ a month for that unless you really like to sweat.
Transport - well forget anything other than a push bike on that salary. A 5 year old, badly maintained Fiat Uno costs S$35,000 at the moment and that will be worth just S$8000 in scrap value when it gets to "retirement" at 10 years old. New car - just forget it. Having said that public transport is OK providing you live near an MRT station and have a tolerance for crowds (a peak times) and body odor (at all times). Water being expensive, washing has become something of a luxury - both clothes and bodies - it would seem.
Food can be cheap if you are prepared to eat local delicacies such as rice and noodles and lots of MonoSodiumGlutamate. "Western" food has become progressively more expensive recently (and it was never that cheap to begin with) due to lower number of western ex-pats and the plummeting rate of exchange against all currencies except, unfortunately in your case, the US $. Beer is $12 a pint or $5.00+ a can. A bottle of spirits is around $70 for 750ml.
A lot of locals are surviving on less than your proposed $$5000 (US$3000) but they have various housing schemes that help them do that. These are, it goes without saying, not available to ex-pats.
Income tax is capped at 22% or so, but don't sweat that on your proposed salary you will be at the lower end. Ministers here are paid S$80K a month, but they are smart - they are in goverment.
Socially it isn't that bad. Singapore is rife with institutionalized racism but if you can handle that and all the problems it brings at work, you can manage. But you will need a while to get used to the local language. Nominally it is English, but it is a form of English unknown to any formalized dictionary. Sometimes it can be bloody hard to understand even after many years of exposure. Feigning deafness is a good ploy since not being able to understand the perfect diction of the taught Queen's English is a gross insult.
I have only given you an outline of the problems as I see them, but you may well see them differently. But if you do come here for that salary - don't say you were not warned.
Knowing what I know now I would not come to Singapore to work in any professional capacity unless I was on a rock solid S$12,000 / month + accomodation. At least on that I could save something to make up for the daily indignities.
DG