I'm looking to create areas where water might go when a river floods its banks. I have a pretty good resolution DEM (5ft^2 for each "square"). I'm not looking for anything super accurate or precise but just so that I could go and check the areas out whenever a flood event occurs on the river. Below is a pictures of what my DEM looks like. I was just going to consider the banks to be where it goes from almost black in color to more of a dark grey (like I said, I'm not looking for anything exact).
I cannot see your image but if your floodplain is nice and flat and the river has low slope then you can try thresholding the raster using symbology.
Alternatively you can use the slope tool in Spatial Analyst (or 3D Analyst if you have access to it) to identify areas of low slope either side of the river. This may help you to identify the floodplain which should be flatter than the valley edges, you can try downsampling your image to 25m or 100m cells to filter out local relief.
If the river has high slope and the other two options are not satisfactory, you could try to take the longitudinal slope out of the DEM by interpolating a new surface from the lowest points in the river and subtracting this from the original DEM. This would leave you with a surface that represents the hieght above the river which you could then threshold. If you have a centreline for your river and you have access to 3D analyst then you can use the Interpolate Shape tool to get z-values for the river from the DEM, then use Trend or some other interpolation to tool to generate a new surface based on your 3D centreline. From there you can use Raster Math to subtract the interpolated surface from the original DEM. Then you could use Contour List to create a contour line at a chosen height above the river.