Here is a breakdown of how often each franchise is selected, by league.
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Franchise	.	5-A	.	5-B	.	5-C	.	5-D	.	Total
A's		1		1		5		2		9
Astros		2		0		0		1		3
Braves		1		0		0		2		3
Cardinals		0		2		2		0		4
Cubs		3		1		1		1		6
Dodgers		1		2		4		4		11
Giants		3		4		3		2		12
Indians		4		8		3		8		23
Mets		0		0		0		1		1
Orioles		0		1		0		0		1
Phillies		1		0		1		0		2
Pirates		1		0		0		0		1
Red Sox		4		4		1		2		11
Reds		0		1		0		0		1
Royals		0		0		1		0		1
Tigers		1		0		1		0		2
White Sox		0		0		1		0		1
Yankees		2		0		1		1		4
Total		24		24		24		24		96

Here a complete list of each franchise selected, sorted by league, then by owner...
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Owner	.	League	.	Franchise
Bansberg		5-A		Red Sox
barracuda3		5-A		Pirates
boogerlips		5-A		Giants
chargingryno		5-A		Phillies
ChitownBluz		5-A		Cubs
d_rock97		5-A		Indians
donaldjtrump		5-A		Yankees
duhbigcat		5-A		Indians
jfranco77		5-A		Indians
just4me		5-A		Braves
markeking		5-A		Red Sox
mattedesa		5-A		Tigers
mickr9		5-A		Yankees
MJDSupporter		5-A		Cubs
mjkrunner		5-A		Dodgers
newarkwilder		5-A		A's
PrimetimeTW		5-A		Astros
Quarantine		5-A		Cubs
Relkcirts		5-A		Giants
rmarksduke		5-A		Red Sox
schwarze		5-A		Giants
Sonofodin52		5-A		Indians
SteveIzzy		5-A		Astros
toddcommish		5-A		Red Sox
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3dayrotation		5-B		Red Sox
alainacath		5-B		Red Sox
asdlfef		5-B		Dodgers
besterateam		5-B		Indians
calhoop		5-B		Cardinals
DCNats4000		5-B		Giants
discodemo		5-B		Indians
ff09		5-B		Cubs
Fsmiley		5-B		Indians
Fusion27s		5-B		Giants
Galveston		5-B		Giants
gworear		5-B		Cardinals
hebdomad		5-B		Red Sox
jbohrman		5-B		Indians
Jdh34		5-B		Indians
jmcraven74		5-B		Red Sox
ledfoot		5-B		Indians
marinerrott		5-B		Indians
mpitt76		5-B		A's
NebHusker		5-B		Dodgers
nordawg		5-B		Orioles
redcped		5-B		Indians
Taxman2008		5-B		Giants
thejuice6		5-B		Reds
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adsmith182		5-C		A's
andricecakes		5-C		Royals
Bill_James47		5-C		Dodgers
billyb1173		5-C		Dodgers
brickster44		5-C		Tigers
buddhagamer		5-C		A's
bullet6464		5-C		A's
contrarian23		5-C		A's
dorkster		5-C		Indians
ejstockman		5-C		Giants
fatboydad54		5-C		Dodgers
firesalt		5-C		Cubs
frank_drebin		5-C		Giants
garmansouth		5-C		Phillies
GeorgeHRuth		5-C		Giants
mllama54		5-C		Indians
redsfive		5-C		White Sox
Ribbentrop		5-C		A's
ronthegenius		5-C		Cardinals
skilly006		5-C		Dodgers
tigerrott		5-C		Red Sox
toysboys		5-C		Cardinals
trd3		5-C		Yankees
vaugheyj		5-C		Indians
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_JJP_		5-D		Indians
AAartist3		5-D		Dodgers
BeAllEndAll		5-D		Dodgers
beauchamp		5-D		Giants
big_dowg		5-D		Red Sox
blackicedcof		5-D		Red Sox
ceno1515		5-D		Dodgers
cubbies84		5-D		Indians
doctorcc		5-D		Dodgers
ericmill16		5-D		Indians
franklynne		5-D		Indians
Fungoes		5-D		Cubs
Jtpsops		5-D		Indians
justinlee_24		5-D		Indians
magicdreamer		5-D		Indians
odalisgagne		5-D		Indians
oldtimer59		5-D		A's
oldtimer59		5-D		A's
Qhadow123		5-D		Braves
RebJebb		5-D		Astros
sford		5-D		Giants
Tammyk		5-D		Braves
tensaver716		5-D		Mets
wstevens07		5-D		Yankees

Same table as above, but sorted by Franchise...
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Owner	.	League	.	Franchise
adsmith182		5-C		A's
buddhagamer		5-C		A's
bullet6464		5-C		A's
contrarian23		5-C		A's
mpitt76		5-B		A's
newarkwilder		5-A		A's
oldtimer59		5-D		A's
oldtimer59		5-D		A's
Ribbentrop		5-C		A's
PrimetimeTW		5-A		Astros
RebJebb		5-D		Astros
SteveIzzy		5-A		Astros
just4me		5-A		Braves
Qhadow123		5-D		Braves
Tammyk		5-D		Braves
calhoop		5-B		Cardinals
gworear		5-B		Cardinals
ronthegenius		5-C		Cardinals
toysboys		5-C		Cardinals
ChitownBluz		5-A		Cubs
ff09		5-B		Cubs
firesalt		5-C		Cubs
Fungoes		5-D		Cubs
MJDSupporter		5-A		Cubs
Quarantine		5-A		Cubs
AAartist3		5-D		Dodgers
asdlfef		5-B		Dodgers
BeAllEndAll		5-D		Dodgers
Bill_James47		5-C		Dodgers
billyb1173		5-C		Dodgers
ceno1515		5-D		Dodgers
doctorcc		5-D		Dodgers
fatboydad54		5-C		Dodgers
mjkrunner		5-A		Dodgers
NebHusker		5-B		Dodgers
skilly006		5-C		Dodgers
beauchamp		5-D		Giants
boogerlips		5-A		Giants
DCNats4000		5-B		Giants
ejstockman		5-C		Giants
frank_drebin		5-C		Giants
Fusion27s		5-B		Giants
Galveston		5-B		Giants
GeorgeHRuth		5-C		Giants
Relkcirts		5-A		Giants
schwarze		5-A		Giants
sford		5-D		Giants
Taxman2008		5-B		Giants
_JJP_		5-D		Indians
besterateam		5-B		Indians
cubbies84		5-D		Indians
d_rock97		5-A		Indians
discodemo		5-B		Indians
dorkster		5-C		Indians
duhbigcat		5-A		Indians
ericmill16		5-D		Indians
franklynne		5-D		Indians
Fsmiley		5-B		Indians
jbohrman		5-B		Indians
Jdh34		5-B		Indians
jfranco77		5-A		Indians
Jtpsops		5-D		Indians
justinlee_24		5-D		Indians
ledfoot		5-B		Indians
magicdreamer		5-D		Indians
marinerrott		5-B		Indians
mllama54		5-C		Indians
odalisgagne		5-D		Indians
redcped		5-B		Indians
Sonofodin52		5-A		Indians
vaugheyj		5-C		Indians
tensaver716		5-D		Mets
nordawg		5-B		Orioles
chargingryno		5-A		Phillies
garmansouth		5-C		Phillies
barracuda3		5-A		Pirates
3dayrotation		5-B		Red Sox
alainacath		5-B		Red Sox
Bansberg		5-A		Red Sox
big_dowg		5-D		Red Sox
blackicedcof		5-D		Red Sox
hebdomad		5-B		Red Sox
jmcraven74		5-B		Red Sox
markeking		5-A		Red Sox
rmarksduke		5-A		Red Sox
tigerrott		5-C		Red Sox
toddcommish		5-A		Red Sox
thejuice6		5-B		Reds
andricecakes		5-C		Royals
brickster44		5-C		Tigers
mattedesa		5-A		Tigers
redsfive		5-C		White Sox
donaldjtrump		5-A		Yankees
mickr9		5-A		Yankees
trd3		5-C		Yankees
wstevens07		5-D		Yankees

I added a tab to the Standings spreadsheet to show how the various franchises are doing with respect to winning%. Note that my original summary (above) listed oldtimer59 twice (A's) and excluded mildnhazy (Indians). This was fixed in the spreadsheet.

Not surprisingly, the Indians are crushing. Some teams selected only once are doing very well (White Sox, Pirates)