alternator output v rpm
If your Alternator is 2 pole it is reasonable to say that the broken engine was running at 3000rpm  making 50Hz.This would be at a reasonably high value of rotor exitation . It is plausible that a micro hydro could run at maybe 170rpm.So yes you could on the face of it charge a 12V lead acid battery.Remember that the Alt was rated for 5KW so that means about 22 Amps RMS current in the copper wire.The rectifier could be some 30 Amp shottkey diodes which are cheap these days .Now you are not out of the woods yet .The DC    volts needed for exiting the rotor wont generally be 12 so count on needing some kind of DCDC convertor.The power needed for excitation is significant and must be checked to make sure that efficiency is still reasonable .Also check your armature wire DCR because copper losses will in percentage terms be much worse than when the machine was making 220VAC .Generally speaking people use permanent magnet type machines for such low volt DC .