As a beginner, would a lump sum investment or monthly investment be more suitable to buy SPDR ETF?

With a Charles Schwab or TD Ameritrade or some other online brokerage in the U.S. ,

given their 0.00 USD commission fees, anything is possible

Your question should really be what is your desired portfolio at this point of time.

Are you looking at a portfolio with 30% equities, 60% bonds, 10% cash/money market fund? (assuming you are low to medium risk)
If yes, then your portfolio should be slowly built up in that proportion.

There are both bonds and stocks (including SPDR STI ETF) on SGX. With $5k per month, you should be comfortable with executing purchase in these ETFs via the low cost stock brokers in Singapore.