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You may assume.. it should have been written clearly if it's other than Singapore dollar (e.g. US dollar 5,000 only, they should have written if it's not Singapore dollar). Secondly, in general companies pay Gross salary in Singapore  (nobody pays net salary unless u work in Middle East countries where many countries don't attached tax into your salary). Here, gross salary means salary before tax. So, read carefully what they are offering and a wise decision that you should clarify your doubts with employer not here, as we don't know what has written in your offer letter. Good luck.

Surya is correct about income tax: No deductions are made by your employer, and you have to pay it in one lump sum after submitting your tax declaration at the end of the year (so do put aside some money for this!). The tax rate for S$5000/month income is about S$2000/year for a resident.
However, if you are contributing to CPF (the local version of social security), this is deducted from your salary by the employer. The current rate is 20% of your gross salary.

Thanks guys. That makes things clearer to me.