If you have access to Spatial Analyst in ArcGIS (or something similar), you can do something like the following:
If you want to generate 'noise' to your DEM, I suggest using the Create Random Raster tool to generate a random raster at the same extent as your SRTM DEM. You can specify the output cell size to 5m or whatever you require. The results of the pixels will be between 0 and 1.0. You can add this to your DEM using the Plus tool ensuring your cell size in the environments is set to the same as your random raster.
If you need to, before you add the DEM and random raster, you can multiply the random raster by a constant using the Times tool. For example, multiplying the random raster by 2 would result in values between 0 and 2.0, which you could then add to your DEM.
That should create sufficient detail that doesn't modify the original DEM too much.