It was more than 5 cards. I tried for 10 and got 9. A business card got away bec I couldn't prove my business address
After the first card or two, I did the free trial thing at myfico.com and it reported that my score was 805.
After reading Dan's summary about the relatively short term impact of credit card inquiries, I figure my score will still be in the upper 700s somewhere, but ... I'm too cheap to pay myfico to find out exactly