A partiton and a filesystem are two different things. The filesystem is what holds the data, so corrupting that is what will lose your data. A partition is just a container, it doesn't use drive space. Deleting a partition could be considered analogous to taking the walls away from a room and leaving the stuff inside (files).

To recover data from a lost partition, all you need to do is recreate the partition and give it the correct type. If a filesystem has overwritten another, you may have lost all of the data, depending on whether or not the FS is journaled (which NTFS is, unfortunately).

The fifth partition is probably lost for good, but it would appear that the sixth has only been deleted so thoretically it should be possible to recreate.