Beaches near Ica

Without a doubt hit Huacachina for sandboarding and swimming pool action. not quite the beach but the amount of sand and chilled out vibe more than makes up for it.

Huacachina is a good place, and is very close to Ica, just 10 minutes drive away. The hostels and hotels there are very reasonably priced. If you want the beach, the safest beach resort south of Lima is a place called "Asia", around Km 90 of the Panamerican highway. It is generally expensive during the high season, as it is where all the Lima wealthy head off to, but now I don`t think you will have a problem finding some place for around U$15 per night. Soyuz bus / Peru bus will drop you off at the Asia turnoff and you can take a moto-taxi from there.

If you are in Ica, Paracas is not too far away.
Definitely worth a visit...if you get off the beaten track, there are pristine beaches, marvelous arches, sea lions, little beach/fishing towns with AMAZING ceviche (couldn't be fresher), check it out!

Actually "5 hours or less from Ica" goes all the way up to Lima.
Anyway, both Paracas and Huacachina are nice, though I'll probably go for the former. There are some nice beaches there, and very good seafood. Moreover, you find the Paracas National Reserve, where you get to see plenty sea lions, penguins, and even some condor (which are said to gide down from the Andes to feed on the sea lion's placenta during the mammal's reproduction period).
Most of the beaches around Lima, at this time of the year, are pretty empty. And given these are artificially built, residential seaside resorts (i.e. not fishing towns or the sort reconverted to tourism), nothing happens there outside summer (traditionally, from new year to easter). One exception could be Pucusana (60km south of Lima), a pintoresque fishing town. But again, I'll go for Paracas.