Are you sure you got control of BITS and BYTES?
When testing your speed with speedtests online, you're measuring BITS per second. When downloading files, your speed is in BYTES per second. As there is 8 bits in a byte - Your download speed "should" equal your speedtest-result /8.
Getting 8mbps on speedtest, would give you 1MB/s download-speed.
Also check your sources. (Local-FTP???)
You should also run different speedtests to verify a result. You will almost never get a 100% correct answer by running a speedtest, but it will give you a pointer.
To answer the question - there is software to monitor your computers bandwidth use, but it's not likely that's the culprit.
My guess is mixed terminology if you say the speed is 5 times higher on speedtest.
Addition: I just did a speedtest on speedtest.net.
In my example, I "should" get a download speed of 32,5MB/s. Now - with that speed there are other things limiting downloads (like disk-speed+++) but it should give me a pointer of what I could expect with hardware that supports it.