I say let them bridge the distance in their relations, if you know what I mean.  
Put an apple pie in the oven, wink wink, nudge nudge.  
Find out if the Pies do shotgun weddings the hard and fun way, as it were.

Even most prude cultures allow marriage of seventh generation relatives.

woopsie, nice try pinkie

Genealogist here.
 
Being fourth cousin to someone means you had a great-grandparent who was first cousin to a great-grandparent of your fourth cousin.
 
Being fourth cousin twice removed describes the relationship between the grandchild of one’s fourth cousin. (If they are the grandchild of my fourth cousin, then they are my fourth cousin, two generations - or twice - removed, and I would be the same to them.)
 
Being fourth cousin twice removed by a fifth cousin is, quite frankly, nonsense, and entirely what I would expect of genealogy being interpreted by Pinkie Pie.

your pony anatomy is adorable!

@Keith Mowz  
Eeyup.
 
Also… I remember it being mentioned on a VSauce video at one point:  
“Every person is (at least) 50th cousins”
 
Also:  
“If you marry a person from the same country and of the same ethnicity there is a 1/5 chance of you having a common ancestor fewer than 10 generations back”
 
‘Course this is way outside the scope for it to matter. But it does mean you can pretty much find a connection with anyone you want, as long as you search hard enough, and far enough back. You’ll probably be able to find that, somehow, Pinkie is like a 58th cousin to Princess Celestia.
 
@Exhumed Legume  
:D

@Sollace  
Basically, four generations back, their ancestors were cousins via marriage. They share no direct ancestry.

@Sollace  
I was looking up this “removed” thing, ended up on that same site… :D
 
If I’m reading this right, “fourth cousin twice removed” by itself would mean, in this case, that one of the Pie sisters’ grandparents is fourth cousin to the Apple siblings.
 
 
The only meaning I can think of for “by” a fifth cousin is, Igneous or Cloudy being a fifth cousin to the Apple siblings.
 
_{Or, most likely, the writer(s) just thought it’d be funny to mince distant relative terminology a little bit, just to make Pinkie’s excitement over being “cousins” with AJ a little bit more absurd.}
 
 
Eh, whatever the case may be, anyone who thinks Marble and Mac are too closely related probably should avoid dating people from their home town, just to be safe.

@Exhumed Legume  
>fourth cousin twice removed by a fifth cousin  
That breaks down to:  
>fourth cousin  
Same great-great-great-grandparents.
 
>twice removed  
There’s a two generation difference in the gaps between yourself and the a common ancestor, and the cousin and that same ancestor.
 
So they are two generations older, or younger than your fourth cousin non-removed.
 
The ‘by a fifth cousin’ doesn’t seem to make any sense though. Maybe there was inbreeding. *shrugs*
 
I think it looks something like this:  
[great-great-great-great-grandmother][great-great-great-great-grandfather]—––[fourth-cousin, twice removed]  
[great-great-great-grandmother][great-great-great-grandfather]–––––––––––[fifth cousin]  
[great-great-grandmother][great-great-grandfather]———–[fourth-cousin][fifth cousin (?)]  
[great-grandmother][great-grandfather]–––––––––––[fourth-cousin, once-removed][spouse]  
[grandmother][grandfather]———————————[fourth-cousin, twice removed][spouse] ->[Applejack]  
[mother][father]  
[Pinkie]
 
 
Source  
And a nice chart
 
Aren’t distant relationships fascinating.

@ObliviaTheChangeling  

^ This. ^
 
Whatever “fourth cousin twice removed by a fifth cousin” means exactly (I get the 4th and 5th cousin parts individually, but the “removed” thing is a literally foreign concept to me), it’s definitely distant enough to not count.

@Background Pony #F116  
You’re kind of a buzzkill, you know that?

@Background Pony #F116  
That’s a rather definite yet weak rebuttal. Care to elaborate?

Whether it would torpedo the ship or not, that’s just an incredibly awkward thing to shout out while your sister is making out with your cousin.

@Parallel Black  

@PonyPon  
That’s because it’s a joke…

@ObliviaTheChangeling  
Word.

@Parallel Black  
good that it doesn’t annoy me, bad that it basically isn’t a defense at all.

So far distant it doesn’t matter. Let them be happy instead of forever wondering what could have been.

@Firefanatic  
Canon never stopped you guys before, so why now?

3
 
There are 3 defenses here.
 
I can still count them.
 
We must try harder.
 
… Uh, clearly incest is not a problem, because pony genes work differently from humans. Yes.  
_{ref: The Cake Twins}

@Meanlucario
 
Nah, I’m just bitter over shipping.

@PonyPon  
The ship is cute and they should incest anyway.
 
How did I do?

@ObliviaTheChangeling  
I keep on saying that, but nobody listens.

@PonyPon  
Allow me to be the first:
 
Even if they are related, the relation is so distant that it doesn’t really matter anyway.