I'm a learning freak, so here's my list:

1. MONSTERS INSIDE ME

2. THE DOCTORS

3. STRANGEST WEATHER ON EARTH

4. WHITE RABBIT PROJECT

5. PARTS UNKNOWN

X-Files
Dark Shadows
Orange is the New Black
Arrested Development
Community

One step beyond
Outer limits (b&w)
Dr Who (yeah from 1963 forward)
Star Trek (you would have thought that by the 23rd century Kirk would have a better phone)
Babylon 5
Basically most of the shows already listed.
I was just thinking of my flickering blue parent from long ago.
Oh yeah Johnny Socko and his flying robot.
Damn gargoyle!

I would keep all but one of your pics, and replace Stranger Things with Orange Is The New Black. We have very similar viewing tastes.

Will and Grace (some of the smartest writers, ever)
Burn Notice
Dexter
Six Feet Under
Ray Donovan

Battlestar Galactica
Blake's seven
Firefly
The world at war
Les Revenants first French season only

Wow! I like your list and have watched all of them. Throw in Supergirl and The Flash, Westworld and the Netflix series Ozark. and you have a good peak at my TV habits.

Handmaids tail (Hulu )
This is us
Shameless
Girls
American horror story
Wentworrh

Here are some Netflix faves
1.Atypical
2.Grace and Frankie
3.Ray Donovan
4.The L word
5.Modern Family
6.The Blacklist

From other sources:
1.Two and a Half Men
2.The Mentalist
3.Monk

Simpsons (seasons 1-10)
30 Rock
South Park (seasons 1-10)
X-Files
Star Trek (original series)

I would want to look further afield at some European tv series too.

Supergirl
Masterchef junior (I love kids)
The good doctor
Big brother
Ghost whisperer

Lots of good choices here and I won't argue with them but Here is one not there. "Wolf Hall", its the Ann Boleyn story from the perspective of Thomas Cromwell. The guy rose from being the son of a blacksmith, to becoming the 2nd most powerful man in England.
This is at a time of great changes. The introduction of Protestantism into the English speaking peoples and subsequently the US. At a time slot relative to where Islam is now (about 1400 years in). With all the factional infighting and bloodshed over dogma .
Beautifully written and filmed, a must see.

In no particular order:

How I Met Your Mother
The Expanse
Rick and Morty
Westworld
Full Metal Alchemist: Brotherhood

I'm not even going to argue that list. Although that is very current-heavy. Let me add a "classic version" in addition, which would be:

1 - The West Wing
2 - All in the Family
3 - MASH
4 - Coupling
5 - Prisoner Cell Block H

In chronological order of premiere:

1. All in the Family
2. St. Elsewhere
3. Northern Exposure
4. The Wire
5. Mad Men

1. Breaking Bad
2. Better call Saul
3. Vikings
4. Game of Thrones
5. Stranger Things

1. Battlestar Galactica (2004)
2. X-Files (and the movies)
3. Firefly (and Serenity)
4. House
5. Star Trek
6. OMG there are so many more asdfkj;askdfjl;asdkkslkdjfslkdjflskdj

1.) Spartacus
2.) Dexter
3.) Game Of Thrones
4.) Sons Of Anarchy
5.) Breaking Bad

No longer on tv but worth finding
Mad Men ( absolutely must)
Tudors ( minimum series)
SO A

Current
Masterpiece Theater Poldark
Orange is the New Black

1. The Venture Bros
2. Leverage
3. Brooklyn 99
4. My Little Pony: Friendship Is Magic
5. Daria

1. Firefly
2. Battlestar Galactica (reboot)
3. Community
4. Breaking Bad
5. Buffy the Vampire Slayer

Game of Thrones
Breaking Bad
Battlestar Galactica
The Expanse
Star Trek - All of them

1 and 2 same, I like the rest of your list a lot too, but for some variety/comedy:
3. Red Dwarf
4. Rick and Morty
5. Shameless

Limiting to 5 might be too difficult.
MASH
Game of Thrones
Dexter
Quantum Leap
House
Monk
Psych
House of Card
Castle
Love Boat
Law & Order SVU
Andy Griffith Show
I Love Lucy
Shameless
Schitt's Creek

So many to choose from....