This is normal and doesn't represent a problem. People tend to think of RAM as being either occupied or free, but that isn't actually the case. A file cache is a perfect example of this.
When you copied that data from the external drive, it had to read the contents into RAM first so it could then write it to the other drive. Copying 5 gigs of data into RAM is a computationally expensive operation. Now what if you wanted to use those files you just copied? The computer is betting that you will, so it kept the copy in RAM around so that it doesn't have pay that cost again if you do.
Now here's the kicker that addresses the heart of your question: Does having 5.66 gigs of data in the file cache really only leave you with 250-400 MB of RAM available? Nope. That 5.66 GB is still free as far as the operating system is concerned. Why? Because the computer can dump that RAM in a nanosecond if it were needed for something else. It is more beneficial for you to have your RAM filled with cached copies of stuff than it is to have it sitting empty doing nothing. The smarter the operating system is about what to cache, the faster your computer is.
Even though that program is telling you the truth about how much RAM is being used, at the same time it is misrepresenting the amount of RAM you have available.