I think that the
Electric type is a pretty good starting point for CAP5. Firstly, it threatens almost all Water-types directly with its STAB attacks, whereas the popular Tentacruel and (to an extent) Gyarados can easily take Grass-type attacks and gain momentum in their various ways. Gastrodon is fodder for a lot of other Sun-mons, while Rotom-W can't really hit mono Electric very well at all in Sunlight, especially if we give it good special bulk or a Water-immunity ability. It also has an inherent lack of weaknesses for Rain teams to abuse, as Ground-type coverage generally isn't very popular on them. Electric typing also blocks Thundurus-T's and Tornadus-I's STAB attacks, which is something that hasn't really been considered that much. This means it'd be pretty reliable as an anti-Water-type and anti-Rain Pokemon, whereas a similar Grass-type would have that weakness to Ice Beam to contend with.
It would also promote the use of Ground-type Pokemon, especially if we make it bulky enough to take non-STAB Earthquakes and survive. While Ground-type Pokemon aren't exactly uncommon, they generally fall in middling to low usage, especially on Rain-teams, so the shift caused by a potent Electric Sun-mon would be quite interesting.
While this looks like a pretty big list, and while Dragon-types aren't directly threatened by Electric-typing, movepool and stat choices can give a number of Dragon-type Pokemon (and a few Ground-types) poor matchups against CAP5, so these issues can be resolved later. Notably, if CAP5 has a decent Special Attack stat, the almost certain presence of Hidden Power Ice on its movesets would significantly affect what Ground- and Dragon-types could and couldn't check or counter it, the extent of which can be controlled during the stat polls. Furthermore, if there's concerns that an Electric CAP5 wouldn't have enough reason to be run on Sun-teams, this can easily be rectified by a (carefully selected) secondary typing, movepool, or ability choices. We don't have to give this thing Thunder, for instance.
Overall, I think that providing CAP5 with Electric typing would be a good starting point, providing an offensive tool for Sun-teams to use against Rain teams while not opening up weaknesses to common coverage moves. If we decide to give CAP5 a secondary typing (we aren't being forced to!), then I'd suggest that it doesn't have a lot of exploitable weaknesses to common moves found on Rain teams. Thus, I think
Ghost,
Fighting,
Dark, and
Psychic, would be the best choices in that order, all having specific, unusual weaknesses that would need to be exploited to OHKO CAP5 if we make it suitably bulky, while each providing intrinsic advantages such as Rapid Spin immunity, Stealth Rock resistance, great coverage vs Lati@s, etc. This would help to encourage the use of lesser used types such as Dark and Ghost, if STAB was necessary for their low base-power moves to OHKO CAP5.
Water secondary typing would be interesting and provides a Water-resistance while only adding a Grass-type weakness, but we'd be heavily in danger of making something that is both usable on Rain teams and promotes Water-types in general. It'd be a very risky path to take, so I'd recommend not going with Water typing, personally.
tl;dr,
Electric would be good mono-typing,
Ghost/Electric would be good for dual-typing, based on previous arguments.
I also think that having a Water-immunity ability is the way to go, as it would definitely make Water-types a liability with more certainty than any typing choice ever could, but this is poll-jumping so I'll drop it for now.