http://goo.gl/dFQrbx
Artist: Frank Sinatra
Title: Fly Me To The Moon

Since this was the first code in this theme, we would start off with dumping the entire code into Google and see what it throws back.
All the top results all mention IATA codes, this combined with resolving the trailing six characters (dFQrbx) to a goo.gl link which gave us the song “Fly me to the moon”, we can assume we’ll need to resolve the IATA codes to their actual airport names.

We found that world-airport-codes.com is a nice reliable search engine for IATA codes.
it gives back detailed airport information which will help a lot with the rest of this theme.

Using the above mentioned website, let us resolve all the IATA codes

Notice how the first letter of the first couple of airports spell out “five“? Looks like we are on the right track!
Take the first letter of each airport:
FIVEJBNTWOABADDONFDEVENRSEVEND
Almost everything fits, there is that part of DEVEN that seems to not fit, so let us fix that error:
FIVEJBNTWOABADDONFSEVENRSEVEND
Substitute the written numbers for the first solve of the theme
5JBN2ABADDONF7R7D

http://goo.gl/vNpUa7
Artist: Simple Minds
Title: Capital City

Repeat the steps we did with the previous code in resolving the IATA codes to their airports.
Keep in mind that the hint mentions capital city.
You will see that the first couple of codes do not give anything useful when taking just their first character, but looking at what countries they are the capital cities of, that brings us closer to a solve. So I am including the country which the airports reside in, in the table below 😉

Noticed that the first letter of the country name is giving us something good?
We can also now determine what the W can mean: Keep the W as they are, or as I did in my original index build up, W = World, which is the capital city of World 😀

Taking the first letter of each country, we get the following:
FOURTQNTWOLIVEHTHREEZTWOG
Simply sub out the numbers for the final solve
4TQN2LIVEH3Z2G

http://goo.gl/UpKjxn
Artist: Alan Jackson
Title: Where I Come From

Since we are within an IATA Codes theme, first see how we can make proper IATA codes from the code that we are given.
Pairs of 3 looks to be good, I made them all upper case for this step just to make it easier to read:
DHR AMS LID RTM AMS DHR RTM LID AMS RTM AMS LID DHR

Looking up the unique codes, we see that all the airports are from The Netherlands, also known as Holland.
Now think back to our hint from the lyric: “Where I come from”
We know Holland is a known keyword, so looks like we have our keyword already, but no pre-/suffix.
Even looking at the distances between the airports did not give any good ranges (everything from 17KM to 109KM apart!)

Let us look at our original code again:
DHRAM sl iDRT ma MSDh RR Tm LIDAM srTm AMSLI dDhR
Notice how we have pairs of 5 characters in the spots where we would expect numbers?
We know that this is one very big hint to Morse!

Let us assume lowercase is a - and uppercase is a ., we get a substitution of
..... -- -... -- ...- .. .- ..... --.- ..... -.-.
Converting this from Morse to text gives us something very useful:
5MBMVIA5Q5C
We know what to do with them Roman numerals!
5MBM6A5Q5C
Combine the keyword with the pre-/suffix for the final solve:
5MBM6hollandA5Q5C

http://goo.gl/5y2o4G
Artist: Silbermond
Title: 1, 2, 3

This one seems to be fairly simple to solve. Numbers are always some order of 123 and the song title confirms that.
We know that IATA codes are always 3 characters long, which matches with the numbers.
What I am assuming now is that the order of the given numbers indicates in what order the IATA code of each airport needs to be written, let us try it out and see what comes from it.
In the table below I am going to list the airport, it’s IATA code, the 123 sequence given and the IATA code written in that sequence.

Well now! See how the re-sequenced IATA codes now spell out numbers? Looks like this was the right path.
Write all the re-sequenced IATA codes in one line
EIGHTQMWFOURDISCOVERYFTWOJTWOP
Sub in the number and we have our final solve!
8QMW4DISCOVERYF2J2P

http://goo.gl/Y4wGMR
Artist: The Clash
Title: North And South

The first step will need to be to determine which IATA codes we have. Notice that each section is dividable by 3, so let us split each section into that.
ATL LHR SXF VIE VVB / IQN PUF TOJ LIS / DDG PSY ABX / HOU / EXT ACE BBU SOB GOI / HAJ CNS XCH IKT / ORD CDG KGL / ADC AAU MHP FKB / CPG AGT YCC VID / TIA CPT BRU SOF / DIG / RMS TBU JFK / KIW TOF RPR TLL LIN / AKL EDI FUN MPM / LCY DME OMR YCV NOV / IAD ZAZ CEP

Now something seems very familiar. Look at how they are grouped.
We have 5 IATA codes in the first section and 5 again in the 5th section. We know one code that always has 5 “things” for numbers! Yupe, that would be Morse! 😀
But how do we turn these IATA codes into Morse? What was the hint? “North and South”, hhmm… where on earth are these airports located?

Let us gather the information for all the airports, including their Latitude and Longitude in our list.
Bare with us here, this list is looooong, I will also include if the Latitude is north or south of the equator (determined by it being either > 0 or < 0) and if the longitude is east or west of the Greenwich line.

Working from the hint and looking at what we gotten from our lookups, let us see what N/S gives when using them as our Morse substitutes:
N N N N S / N N N N / N S S / N / N N N N N / N S S N / N N S / S S N N / S S N N / N S N N / N / N S N / S N N N N / S N S S / N N N N S / N N S
Taking N as . and S as - and / as separator, we get
....- .... .-- . ..... .--. ..- --.. --.. .-.. . .-. -.... -.-- ....- ..-
Converting from Morse to text
4HWE5PUZZLER6Y4U
Ha! There we go, all done with this one.

http://goo.gl/iB58LM
Artist: Less than Jake
Title: Do the math

“Do the math“, that points to the IATA Codes resolving into something that we can do math with, probably in combination with the numbers.
Let us split the IATA codes and numbers so we have a better overview.
ATL 20 PEK 34 LHR 42 HND 64 ORD 15 LAX 34 CDG 51 DFW 40 CGK 57 DXB 56 FRA 26 HKG 52 DEN 22 BKK 63

Looking up the different airports and attempting various calculations with their Latitudes, Longitudes, Timezones, Telephone numbers, etc brings us to no usable code.
Taking a different approach, forget about the airports and have a look at the codes themselves.
We always have 3 characters, we know that we could convert each character to either Decimal, Hex, Octal, Binary and even Alphabet Indexes.
Doing the calculations with Dec, Hex, Oct and Binary brings us not a single waypoint closer to our destination, but the Alphabet index seems promising!
If we take the alphabet index of each character, add them together and then add the number following each code to it, we get well within the ranges for decimal to text conversion.

Take our final values
53 66 80 90 52 71 65 73 78 86 51 78 45 87
and convert them to text
5BPZ4GAINV3N-W

Hhmm, something doesn’t look right there.
After some bruting of that -, we find that the right number is 7, which was decimal 54,
and such the final solve was:
5BPZ4GAINV3N7W

http://goo.gl/tcYRYf
Artist: Sevendust
Title: Letters