Across:
1. Cooks entertaining women athletes (8) SWIMMERS = S(W)IMMERS
5/35. What, a Magritte painting is not about amazing drop & iconic peak? (4,2,8) PICO DO PRÍNCIPE = PI(DROPICONIC*)PE
10. Old, Old Dominion's counterparts to [swimmers]? (3) OVA = O (Old) + VA (Old Dominion = Virginia)
11. Organisation headquartered in Manhattan: Agent was offended by being not included in portrayal (13) UNREPRESENTED = UN + REP + RESENTED
13. Type of business in which people can sell shares of body parts to comedian Louis and other associated people (5,5,7) JOINT STOCK COMPANY = JOINTS + TO + CK + COMPANY
14. Music for dancing mazurka not entirely boycotted by king (5) MUZAK = MAZU(-r)K(-a)*
16. Decorated soldier essentially unseated leader in decline (3,2) DID UP = DI(_D_ + U_)P
17. More than one saying "Yes, finally!" after this horror film hit the theatres in 2004 (4) SAWS = SAW (this horror film…) + (-ye)S
20. Bohemian flower enthusiast listing biological and environmental tips (4) ELBE = E_ L_ B_ E_
21. Measures against cyber attack extremely efficacious (5) DOSES = DOS (cyber attack) + E_S
22. Ski with detainees to see someone from the Southern Alps? (4) KIWI = _KI WI_
25. Festive cockatoo's tail trimmed (4) GALA = GALA(-h)
26. Its regular use can prevent health issues such as gingivitis and fluorine deficiency (5) FLOSS = F (fluorine) + LOSS (deficiency)
28. OPEC utilises downtown headquarters? That's better (5) OUTDO = O_ + UT_ + DO_
29. Man pursued by fake monster – he is caught by stray elastic band (8,9) SYMPHONY ORCHESTRA = + (M + PHONY + ORC + HE’S) in STRAY*
32. To intensify love in romance, order revealing top (5,8) MOUNT CAMEROON = MOUINTMOUNT (to intensify) + ROMANCE* containing O (love)
33. Style of music that's dryly humorous according to the audience (3) RAI = “wry”
34. Poor man's symbol painted on Russian tanks rates badly in the West (6) ERSATZ = RATES* + Z (symbol painted on Russian tanks)
35. (See 5 across)
Down:
1. Who's produced woollen sweater for trained horse? (4,6) SHOW JUMPER = WHOS* + JUMPER (woollen sweater)
2. Backers to order CIA HQ to feed Second Gulf War combatant, perhaps (5) IRAQI = I(_R _A _Q)I
3. Peak of UK autonomy stripped in rebellion (5,3) MOUNT OKA = UK(-a)UTONOM(-y)*
4. Film, starring Bruce Willis, that's about Euro sailor running to the north, given new classification (7) REARATED = RE(E+TAR)<D
6. First convict's starting to break out, with second in tow, getting outdoor views of the Siberian winter? (9) ICESCAPES = I (First) + C_ + ESCAPE + S (second)
7. Give overweight Poles possibly endless dish made out of potatoes in public (8) OVERMAST = OVER(MAS(-h))T
8. Ancient port, after losing northern entrance, is not very revolutionary (5) OSTIA = AI(-n)TSO<
9. Current Nordic epic given happy ending instead of its original one (4) EDDY = EDD(a → _Y)
12. Revolutionary intellectual property legislation one old book displays (it is highly prominent) (4,2,3,4) PICO DE SAO TOME = IP< + CODES (legislation) + A (one) + O (old) + TOME (book)
15. A wild thing that's almost completely shameless, with feet raised above head (5) ZEBRA = BRAZE(-n) with ZE put before BRA
18. Part of a person's body is buried inside temple (5) WAIST = WA(IS)T
19. Gladys is seen, with sociable stranger following, closer to Bishop Peak (4,6) PICO BASILE = (-bisho)P + I (Gladys) + SOCIABLE*
21. Conclusion for one rebellious party (9) DEFENDANT = DEF(i → END)ANT (thanks to @user39583 in comments)
23. Couple's being cut by Argentine blades (8) MACHETES = MA(CHE)TES
24. "Aim at his head!" – Russian special police surrounding one of the Germans (4,2,2) HOME IN ON = H(-is) + OM(EIN)ON
27. Mark told to get help (7) SUCCOUR = “sucker”
29. Scoring using headers? That is associated with Mohamed Salah's sport (4) SUMO = S_ U_ + MO (Mohamed Salah)
30. Violet from Auvergne's picked up (5) MAUVE = _M AUVE_
31. Techies from Texas initially invited to cross Golden Gate (5) TORII = T(OR)I + I(-nvited)
