Feel the excitement!

2,539,798.  Approximately.  I think.  Maybe.  Here’s what I did to get there.

First, the Census department has put together some nice pre-digested block layers, they include the total population for the blocks so you don’t have to compile that data yourself.

Second, create a 5 mile (acutally I used 8046.72 meters because my data in a UTM projection) buffer around my brewery points.  Shp2pgsql, use it to shove the buffers into a PostGIS database and call the layer buffer_5mile.  Fun!

Third, load the block data into QGIS and add a numeric field (I used totarea) to store the area of the blocks.  Use shp2pgsql to reproject the census data to match your buffers and load the results into PostGIS.  I called my layer block_pop.

Fourth, update that new area field with

UPDATE block_pop SET totarea = st_area(geom);

Fifth, to get an estimate of the population within the buffers use:

SELECT 
round(sum(c.pop10*(ST_Area(ST_Intersection(c.geom, b.the_geom))) / c.totarea)) 
FROM
(SELECT ST_Union(geom) as the_geom FROM buffer_5mile) as b, block_pop c
WHERE ST_Intersects(the_geom, c.geom);

Bam.  You done.