Solution to 5D has been deliberately left unsolved and is to be answered only by a non-regular / novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
ACROSS
1 Husband and wife sharing dessert hamper (6) THWART {T{H}{W}ART}
4 He needs leadership to suppress independent university? (6) HELIUM {HEL{I}{U}M}
9 Death wish? (4) WILL [C&DD]
11 Warrior takes a day to capture Arizona (6) AMAZON {A}{M{AZ}ON}
12 Subjects missing Oscar succeed reflecting on society (8) DWELLERS {Do WELL}{RE<=}{S}
13 Where some connect virtually all day long? (9) CHATROOMS [CD]
15 Princess acquires the Spanish restaurant (4) DELI {D{EL}I}
16 Japanese wine with one in place of English writer (4) SAKI SAK(-e+i)I
17 As per Spooner, brand popular for portable furniture (9) CAMPSTOOL (~stamp cool to campstool)
24 Review study probing liver? (10) RECONSIDER {RE{CON}SIDER}
26 Have three letters in sequence in front to baffle (6) DEFEAT {DEF}{EAT}
27 Impressed others with the man’s daughter (6) ETCHED {ETC}{HE}{D}
DOWN
1 After overwhelming Italy, surpass Hungary for victory (7) TRIUMPH {TR{I}UMP}{H}
2 Last letter following say Disney’s dance (5) WALTZ {WALT}{Z}
3 Routine mostly affected with new strike (3,4) RUN INTO {ROUTINe+N}*
5 Large woman’s light here? (6) E?E?E? (Addendum - ELEVEN Definition by example - See comments)
6 Current report by doctor etc. makes sense (9) INTELLECT {IN}{TELL|}{ETC*}
8 Day America’s dream was set to take on Cinema’s top honours (7,6) ACADEMY AWARDS {DAY+A+DREAM+WAS+Ci...a}* &lit
16 Reverend’s tiny source for marine alga, say (7) SEAWEED (~wee seed to seaweed)
18 Favourite wraps from fried fish (7) POMFRET {P{FROM*}ET}
19 Cook greens initially boiled as required (7) OBLIGED {Gr...s+BOILED}*
20 Almost all MPs regularly sucking blood (6) PLASMA {AlMoSt+AlL+mPs}<=
23 Metal’s tip poking bruised this worker (5) SMITH {S{Me..l}ITH}
Reference List
Husband = H, Wife = W, Independent = I, University = U, Old = O, Oscar = O, On = RE, Society = S, The in Spanish = EL, English = E, Ocean = O, Daughter = D, Italy = I, Hungary = H, New = N, America = A