As others have said, you can have a total of 4 primary partitions on an MBR disk. This means you must either delete one of your partitions or convert it into a logical partition to install Linux in a conventional dual-boot approach. Another option is to buy another disk and install Linux on it rather than on your current disk.
Your Lenovo recovery partition probably contains the equivalent of installation DVDs. You may have a program under Windows that will create a set of recovery DVDs from that partition's contents. If so, one approach to solving your problem is to run this tool and then delete the Lenovo recovery partition, since the DVDs now take its place as an emergency recovery tool. You can then resize your
C: drive and run the Linux installer, which should be able to create an extended partition and as many logical partitions in the free space as you need.
Another approach is to convert at least one partition from primary to logical form. My FixParts program can do this, although it can't resize or move partitions, and you'll need to do this to get everything working, so if you use FixParts you'll have to switch between it and at least one other tool. There are also some third-party Windows tools that can do the primary-to-logical conversion, but I don't happen to have any URLs handy. The biggest problem with this approach is that some partitions need to be primary. This is true of your
C: drive, and probably of your Lenovo recovery partition. I'm not sure about the others. Since all logical partitions must be contiguous (they all reside inside a single extended partition), this means you may have to do more juggling of partitions to get something that works.
Whatever you do, don't try to create Linux partitions in Windows. The Linux installer can do this quite well, and with no risk that you'll accidentally switch from a standard partitioning setup to a "dynamic disk" setup, which is Windows-specific and will create another hurdle to overcome.
Any approach you try is not without risks; resizing, moving, and otherwise adjusting partitions can go horribly wrong. Thus, I strongly recommend you back up your entire disk before proceeding.