I have a shapefile of survey control points (WGS 84) from the public domain provided by my local municipality. I'm using a GeoXH with a zephyr antenna. I have my coordinate system set to WGS 1984. I'm getting 4.5" accuracy (post processed) when I'm recording my test point.

I then take this data back to Trimble Pathfinder Office, post process it using a station about 3 miles from where the points were taken. Pathfinder Office is configured to have WGS 1984 coordinates. I then export this data to a shapefile (without a projection).

Using QGIS (2.18) I start a new project, select WGS 84 (EPSG: 4326), and load my city provided data. I then load my test points (3 taken on tripod over one of the city's monuments). I then load my shapefile, selecting WGS 84. And my data is off by 5 ft (west, and a little north).

Any idea what I'm doing wrong?