I think you'll find that the 5volt @ 2.5Amps will be for the peltier device. It will require a PWM,(pulse width modulation), supply if it hasn't already got one. Depends on how it's set up. If you want to regulate the temp., then you'll need the PWM. If not regulated, then straight DC is O.K., but this will be a constant drain on the battery. Methinks this will not be a field unit, more a home observatory. As they stated in their blurb, an old computer power supply, running off 240 volts, would be more than adequate.
Really, not enough technical/camera info. available without further inquiries.
Have attached peltier details & parts list, from 'Silicon Chip' magazine.
HTH.
L.
ps. The kit is/was avail. from Oatley Electronics for $15.00.