What does "floating [...] 3 years" mean? If it's a floating-rate loan, then "3 years" anything doesn't make sense.
As written it doesn't make sense, but sometimes a mortgage lender will do this sort of thing:
First 3 years: floating rate pegged at X% over reference rate Z (currently 1.8%)
Thereafter: floating rate pegged at X%+Y% over reference rate Z
So it's a floating rate throughout, but during the first 3 years there's a discount. There can be all sorts of "exotic" interest rate formulas, and most of them are pretty dumb.
I too like the 2.0%/5 year offer, but I too want to understand what the interest rate peg is. If it's a SIBOR or SGS peg, and if the 6th year onward is a reasonable markup to the peg, then it looks like a good mortgage to me.
(Also, that fixed-rate loan will probably convert to a floating-rate loan after the 5-year period. In Singapore, and most other countries, "fixed rate" mortgages actually convert to a floating rate after the fixed-rate period; only in a few countries (the US and France are the ones I know of) can you get an actual 30-year fixed-rate mortgage.)
To elaborate a bit, while floating rate mortgages (called "Adjustable Rate Mortgages") are available, the
standard mortgage in the United States is the 30 year fixed rate mortgage. According to Bankrate.com, as I write this, there's a U.S. mortgage lender that's offering a 30 year fixed mortgage at just a little under 3.5% APR and with 0 points. ("Points" refers to a possible sales charge for the mortgage. For example, if the lender charges 1 point, then the borrower would have to pay or possibly finance a US$5,000 origination fee on a US$500,000 mortgage. Obviously a 0 point mortgage is desirable, other things being equal.)
With a 30 year fixed rate mortgage you're often able to refinance the mortgage if/when interest rates fall substantially. There are quite a few people with ~3.0% interest mortgages right now with 20+ years to run, and they're really happy (and should be). Mortgage interest can also sometimes reduce your U.S. income tax bill, although that possible tax benefit has been tempered within the past couple years. (In Singapore mortgage interest can only help reduce your income tax bill on property that you rent out, not for owner-occupied homes.)
There is one quasi-fixed interest rate mortgage in Singapore: the HDB loan, at 2.6%. HDB loans are technically floating rate, but they've been pegged at the floor rate for a long time and stand a high likelihood of staying there. If the HDB loan rate ever rises above its floor, it'll only do so at the same time the CPF Ordinary Account interest rate rises above its floor, in lockstep. So you're very well defended against rate shocks with HDB loans.