I think rozcietrzewiacz found the main thig that's bothering you. Your call to
df is not reporting information about the new partition you created, it's reporting information about the “none” filesystem that's mounted on
/dev. This is an in-memory filesystem that exists solely to host device files. You would see the same output from
df /dev or
df /path/to/file normally reports information about the filesystem containing the specified file; that's what's happening here, because you haven't mounted
/dev/sda5. There's an exception: if you supply the path to a mounted device, then
df reports information about the filesystem on that device.
There's a second issue: you've apparently run
fdisk /dev/sda1. Don't do that, it won't work. You can't create partitions inside partitions that way. (Well, you can, but Linux won't see them.) You need to run
fdisk /dev/sda to create partitions on
/dev/sda, and apparently you already have partitions there. It's not clear how you want to allocate space on your disk; make sure you know what you're doing if there's other data on the disk that you don't want to lose. Check that your backups are up-to-date!
Feel free to ask for more help on this site. But please copy-paste output as text, not as images (which are hard to read and can't be searched) and provide full session transcripts (e.g. show what command you ran in addition to the output of the command). As a starting point, if you're confused on how to split up your disk, show the output of
fdisk -l /dev/sda and explain what the currently existing partitions contain and how you want to reallocate space.
At this point, I recommend reading this answer for background, at least the section about mounting.
Creating a partition defines an area on the disk; it doesn't write anything inside this area. At this point, you should create a partition (type
83) using up most of the disk, and a second partition (type
82) using a couple of GB for swap. On the bigger partition, the second step is to create a filesystem with
mkfs.ext2. Once you've done that, you'll be able to mount that filesystem, e.g. with
mount /dev/sda1 /mnt.