Carbon composition resistors dissipating significant power can 'cook' the binder and decrease in resistance till they overheat and burn up, and when they do so, can do significant damage to the board and surrounding parts.
So that's the same as saying a 3W *carbon* resistor isn't really up to its spec, or it's the failure mode that worries you? I would be increasing the total wattage from 5W to 6W, since the original 5W resistor burnt (actually, 2 of them burnt, and they were in series with nothing else in between, which I find rather odd but I don't see any other problem on the board and it works).
The main reason for the swap is actually that I can't get the original resistors in time and budget, but it wouldn't hurt to increase wattage a little too.
Generally speaking, replacing a 5W part with a lower-rated 3W part is not a good idea. If the previous part failed from heat, its a REALLY BAD idea.
Now if the replacement resisters were 3W appropriate values in parallel (making it a 6W replacement), you might be ok.
I don't see a difference using a series or parallel configuration, the idea was to use 2 x 3W resistors in series, so that's 6W, each resistor with half the value of the original one, of course.