Strominger and Vafa have used D-brane technology to identify and preci
sely count the degenerate quantum states responsible for the entropy o
f certain extremal, BPS-saturated black holes. Here we give a Type-II
D-brane description of a class of extremal and non-extremal five-dimen
sional Reissner-Nordstrom solutions and identify a corresponding set o
f degenerate D-brane configurations. We use this information to do a s
tring theory calculation of the entropy, radiation rate and ''Hawking'
' temperature. The results agree perfectly with standard Hawking resul
ts for the corresponding nearly extremal Reissner-Nordstrom black hole
s. Although these calculations suffer from open-string strong coupling
problems, we give some reasons to believe that they are nonetheless q
ualitatively reliable. In this optimistic scenario there would be no '
'information loss'' in black hole quantum evolution.