Your fourth partition needs to be an extended partition and not primary.
Then inside that space you can create as many partitions as you like. My
setup has 17 partitions. :

How do I create an Extended partition with GParted? That option is
greyed out when I create a new partition.

Via a Linux Live CD or USB perhaps.

I'm runing Gparted from the live CD. The Extended option is greyed out.
Is that not an option using the Live CD?

Find the actual full Gparted iso (it's listed on distrowatch.com), burn it
and boot with it.

You aren't using a wubi install are you? That goes by a whole different set
of rules.

I burned the Gparted iso and now I see the option for creating an
Extended partition.

Another question. Do I first create the Primary partition and then an
Extended partition with other partitions inside that?

Yes, as far as I recall you can't create an Extended Partition until you
have at least one Primary Partition. Create your Logical Partitions inside
the Extended Partition.

It should work from the Live CD. I do it all of the time when I install new
distros. If it is greyed out then perhaps you have some pending changes that
need to be applied first.

The restriction to 4 primary partitions is part of the old BIOS, now
removed in the new Unified Extensible Firmware Interface.

If there are fewer than 4 BIOS partitions an Extended partition can be
created. This cannot be used by itself but can contain an (almost)
unlimited number of logical partitions. These function the same as primary
partitions and are indistinguishable from primary partitions to the end
user.

At least that's what I taught my students 15 years ago, if memory serves me
correctly!

All great advice. I am not going to add any advice. I chimed in because
of what some / most computer manufacturers were doing a couple of years ago.

On many of the machines I installed Ubuntu on, the hard drive was
already set-up with 4 primary partitions. One for the manufacturers
tools. a second for the windows backup image(the one you wanted to copy
to CDs so you could re-install windows. One for the windows partition.
Can't remember what the other one was used for. When installing Linux I
would have to delete the tools partition (most of the time available
online). I then needed an extended partition that I could install any
number of Distributions within. If desired I could put a home partition
in there too.

Lots of good information re partitioning but I'd add in that perhaps
80Gb is a touch on the small side to partition in that way and you'll
have some difficult choices about the sizes to allocate. A better way
would be to use virtual OS's if all you are wanting to do is try out
multiple distro's and Virtual Box is excellent for that.

This is the link for the Gparted manual:
gparted.sourceforge.net/display-doc.php

Read on Selecting Unallocated Space.

If this is not helpful then please post again telling us what it looks like
so far. What you have. Sizes, formats, etc and order.