Five hours ain't much time to cover this city, but I'll try to summarize:
In terms of inclines, the Duquesne Incline has a better view, but there's nothing but a parking lot at its base, and the area of Grandview at the top is pretty lame, with a handful of expensive, underwhelming restaurants. Use the Monongahela Incline instead. It's just a few blocks from
a number of scenic overlooks, and
Shiloh Street is a much nicer business district to explore.
In terms of downtown, one of the lesser known museums is the Fort Pitt Museum. It's tucked away in the reconstructed bastion of the old British fort (the fort itself is gone, though
a 1764 blockhouse remains). Walking around Point State Park is also nice. Nicest street to walk down by far is Penn Avenue, where a lot of the theaters/event venues are located, and
a lot of 19th/early 20th century walkups have been preserved.
Most of the museum action, though, is on the North Side. There's so many musuems here, from the National Aviary to the Andy Warhol Center. My favorite though, if you go a bit more afield, is the
Mattress Factory - a great museum of installation art. While you're there, swing a few blocks away to check out
Randyland, as it needs to be seen in person.
I'd not go to Phipps on such a limited time. Oakland necessitates getting on a bus, and while buses come frequently, there's really not that much else to see unless you want to go to the Carnegie Museums (which are nice, but an all-day thing) or just walk around looking at the civic architecture.
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