Was thinking the same thing, that gen head seems a little large for that engine... If you are wiring it back into your existing panel, you will have to bring in 240 as the existing 120V breakers are(or should be) spread equally across both legs of your existing 240 power input(2 legs of 120). So if you bring in only 120, you will only be able to power half the circuits in your panel.
One of the hazards of running a generator head that is way too large, is that it is quite easy to load the generator head way beyond the engines ability to maintain RPM. This can quickly lead to a brownout which could damage equipment. One way to deal with this is to have that main backfeed breaker sized to the engines output capability, not the generators output capability. SO 10KW divided by 240V is 41Amps. 5KW divided by 240V is 20A, so you should put the 20A(or even smaller) breaker in place to help limit the potential load placed on the generator. Way better to pop a circuit breaker and go dark, than to overload and go brown...