I since noticed in your signature that you are running 5.07 so you will not have the backup feature on that version so before you uninstall make a copy of your Hoster data folder.
On 5.07 it would normally be found in C:\MTU, copy the Hoster folder to a USB stick or skydrive or something that you can easily transfer to your new computer. After installing the main program on your new computer open the C:\\MTU folder and rename that Hoster folder, example to Hosterold, just as a backup, then paste the copy from the other computer into the MTU folder as a replacement of the one you re named.
If all works correct after doing this, then at some time you can delete the renamed folder.
For this to all work correct your music folders must follow the same file paths as used before, so if your music was on drive E then you must set your external music drive to E for the new computer.
Instructions to change the drive letter can be found here:
http://www.mtu.com/faq-test.php?article=4
To install Hoster on a new computer you must first uninstall from the existing computer while your connected to the internet to register the removal with MTU. Unless you still have an extra install available for your version.
Then you need the original hoster507setup.ex file to install on your new computer, if you can't find this then look in your account and see if it shows there for download or you may be able to download it from this page:
http://www.mtu.com/upgrades/hoster.htm
In the install process you will have to enter the exact registration and email address as used previously but that should all show in your account.
If your new computer is Windows 8 in some cases there can be problems using 5.07 to do with where the data folder installs. this was corrected in version 5.09 I believe which moves the data folder to a new location.
Yours might work OK but until you try can't say for sure. That is why in my first post I asked which version you had as the instructions would be different.