With the Live CD, I couldn't delete the sda5 partition, the "delete" was grayed out. In fact, a lot of things were grayed out in the partition editor: new, delete, etc.
However, I load up another Live CD, Xubuntu, and all these options were available. I manage to delete sda5 and after a reboot with Linux Mint Live CD, this time,the partitions were available. No less than 15 minutes later, Linux Mint was up and running!
I think it would have worked with GParted Live CD, but I didn't have this.
Thank you markcynt for your assistance!