Is the synchronization process supposed to be downloading at less than 5kB/s?
The synchronization process may be slow on slow computers - it does not only rely on bandwidth. After downloading a chunk of blocks from various peers, the Client needs to verify every transaction in them, which is a very CPU intensive task. If you have a slow computer, this will be the bottleneck - you will spend a lot of time verifying the block and only a little downloading them, making the average download speed small.