That's a VERY loaded topic on this board...but 27610 is among the lower-income zips in town, if not the lowest. 27604 has areas like that, too, but also some very desirable, Historic areas, and is much harder to classify. Search the forum and you'll find the old thread.
The "old money" neighborhoods in Raleigh are often found in 27608 and 27605; new "high-ticket" neighborhoods are often on the North of town around 27614, -15, -16.
But, bottom line, you can't really use arbitrary geographic designations like zip codes for this kind of decision.