A Cryptic Property

Question

^{An entry in Fortnightly Topic Challenge #48: Unusual tag mix}

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After solving the following cryptic clues, find the following properties:

1. A major property that all ten words share.
2. A minor property shared by the words in one set, but not the other.

Group 1

1. Round, crooked grin (4)
2. Half-baked trifles accomodating upper class's return (5)
3. Contact the old university heads before church (5)
4. Mean queen following Penny (6)
5. Floating motion around two different motorways (8)

Group 2

1. Youthful graduate at hand (4)
2. Wandering nomad meets unknown from beginning of week (6)
3. Crowds in somber assembly back peacekeepers instead of nothing (7)
4. Lower poles around distant, enclosing gas (8)
5. Sour, ripe bananas from manager (8)

Answer 1

The Clues – Group 1

Round, crooked grin (4)
  — RING = GRIN* ("crooked")

Half-baked trifles accomodating upper class's return (5)
  — FRUIT = U (upper class) in (TRIF(les))* ("half-baked", or 4/7-"baked", more like)

Contact the old university heads before church (5)
  — TOUCH = T(he) O(ld) U(niversity) + CH (Church)

Mean queen following Penny (6)
  — CENTER = CENT (Penny) + ER (Elizabeth Regina)

Floating motion around two different motorways (8)
  — SWIMMING = M + MI (two motorways) in SWI.NG

The Clues – Group 2

Youthful graduate at hand (4)
  — BABY = B.A. (graduate) + BY (at hand)

Wandering nomad meets unknown from beginning of week (6)
  — MONDAY = NOMAD* ("wandering") + Y (typical unknown in algebra)

Crowds in somber assembly back peacekeepers instead of nothing (7)
  — NUMBERS = S(O > UN)MBER* ("assembly"; the UN are the peacekeepers)

Lower poles around distant, enclosing gas (8)
  — SOUTHERN = H (hydrogen, "gas") in OUT.ER ("distant" ), all in S.N ("poles")

Sour, ripe bananas from manager (8)
  — SUPERIOR = (SOUR RIPE)* ("bananas")

The property all words share:

They are all one item in a set of five:

Five fingers on a hand: Thumb, index, middle, ring and little finger
Five groups of food: fruit, vegetables, grains, protein and dairy
The five senses: sight, hearing, smell, touch and taste.
Five basketball positions: center, power forward, small forward, point guard and shooting guard.
Modern pentathlon: fencing, swimming, show jumping, pistol shooting and cross-country running

Five Spice Girls: Scary Spice, Sporty Spice, Baby Spice, Ginger Spice and Posh Spice
Five workdays: Monday, Tuesday, Wednesday, Thursday, Friday
Five Books of Moses: Genesis, Exodus, Leviticus, Numbers and Deuteronomy
Five Oceans: Atlantic Ocean, Pacific Ocean, Indian Ocean, Arctic Ocean and Southern Ocean.
Five Great Lakes: Lake Superior, Lake Michigan, Lake Huron, Lake Erie and Lake Ontario

What differs between the two groups:

The items in Group 2 are proper names and the items in Group 1 are just regular nouns.

High fives to:

hexomino, who solved 2.4.