Looking at the installation order on their website, it states the following:

CC3 and older add-ons


1. Install CC3 into its own folder

2. Skip compatibility updates that you have the CC3 versions of (DD3, SS1v3,
SS1v3 or Cities!).

3. Install the remaining compatibility updates (City Designer, Dungeon
Designer, Character Artist, Dioramas, Perspectives, Cosmographer, Symbol Set
1, Symbols Set 2 and Symbols Set 3) in any order.
4. Now install any version 3 add-ons you have (DD3, SS1v3, CC2v3 and
SM:Cities!) in any order.

5. Check your CC3's Help Menu >> About. If the version is less than
3.18, download and install the update available from the registration
page.


What it does not state is when you should have any of the older stuff Installed (i.e. CD2, or DD2 or CHarater Artist etc.)

These actually cannot be installed AFTER the update, but before the update.

So, for City Designer, install City Designer Pro AND THEN run the compatibility update for it.

You are correct in assuming you do not need to install patch 3 and then Patch 5 as Patch 5 would have everything from previous patches already present in it.

I hope this helps.

Also, after installing each piece of software, just start it then exit it, as sometimes it needs to be run once for the machine to recognize it is there (it needs to update the registry files)