Its most likely your source shapefile is not in the coord system that you think it is in, or isn't set properly.
Lets test this.
QGIS is able to reprojects data onto the map, on the fly.
That is, if you have two data sources of different projections, QGIS will automatically project them to be 'in the correct spot' on the map.
So if you have
- Raster as WGS84
- Shapefile as epsg=3005
- Set your project coord system to be WGS84
Then QGIS will automatically reproject your shapefile from 3005, to WGS84 for map display purposes only. Note that it doesn't save the reprojected data, it just does it on the fly for the map.
Now - Does your data look in the right place? Is the shapefile showing the data in the right spot on the map? If not, then probably the shapefiles source coord system is not 3005.
Lets check. Right click on the data in the layer list > Properties > Information tab - What's it say there under the Coord System section? Not 3005? Invalid? Check this here.
Its possible your file hasn't had the coord system set properly, so you can do this using the 'Assign Projection' tool.
But if after you do all that, and the on-the-fly reprojection doesn't work, then it means that data is not in 3005.
Edits
If the on the fly reprojection does work, then it just means that somewhere you have made a mistake with the reprojection and export process.
- In the Reproject tool, make sure you select the same WGS coord system that the raster file is set at - that is the same EPSG number (as there are many WGS84 projections).
- In the Reproject tool you can specify the output file, path and type at the bottom of the GUI. Do this. This is 'saving the output shapefile'.