Ran out of primary partitions, want to install another system

Yes, it's possible. My FixParts program will do the job, with some caveats. Most notably, you need at least one unallocated sector immediately preceding each to-be-logical partition. If such a gap doesn't exist, you can shrink the preceding partition by a small amount using GParted before using FixParts. Some Windows tools can also do the job, but I don't know offhand if any of them can handle Linux partitions.

Another option, if you're using a recent computer that supports EFI, is to convert the disk from MBR to GPT form, install Windows in EFI mode, and convert Linux to boot in EFI mode. This is likely to take more effort than the first approach, though. If you care to try it, gdisk can do the MBR-to-GPT conversion.

Actually you're fine. Based on the fdisk data you posted, sda4 is an extended partition that contains just one logical partition (sda5). You should be able to shrink sda5 and create an arbitrary number of new logical partitions next to it.

I recommend booting into a GParted Live session and using gparted to shrink sda5 and create your new partitions in the unocuppied space.