I have two generators rated at 5 KW each. I know how to phase and put the
two in parallel while they are both running. The question is will they stay
in sync and put out 10 kw if needed ?

I know the Honda generators have a parallel cord, but think that is for the
inverter type. The ones I have are made by two differant companies and just
the inexpensive kind that sell for around $ 600 to $ 800 at most stores.