I couldn't find the Billboard charts for May 1966. Here is a play list from Billboard Top Pop Hits: 1966-5 compilation albums released by Rhino Records to give some perspective of what was hot during the time of the Pet Sounds release. These are singles throughout that year.
1."She's Just My Style" Gary Lewis & the Playboys
2."Red Rubber Ball" Cyrkle
3."No Matter What Shape (Your Stomach's In)" T Bones
4."Ballad of the Green Berets" Ssgt. Barry Sadler
5."Sloop John B" Beach Boys
6."Sunshine Superman" Donovan
7."Daydream" Lovin' Spoonful
8."Winchester Cathedral" New Vaudeville Band
9."Cherish" The Association
10."Last Train to Clarksville" Monkees
and here is 1965...
1."The Name Game" - Shirley Ellis
2."A Lover's Concerto" - The Toys
3."This Diamond Ring" - Gary Lewis & the Playboys
4."Help Me, Rhonda" - Beach Boys
5."You've Lost That Lovin' Feelin'" - The Righteous Brothers
6."Wooly Bully" - Sam the Sham & the Pharaohs
7."1-2-3" - Len Barry
8."Treat Her Right" - Roy Head and The Traits
9."I Got You Babe" - Sonny & Cher
10."Eve Of Destruction" - Barry McGuire
This may help...
Happy Listening!
1."She's Just My Style" Gary Lewis & the Playboys
2."Red Rubber Ball" Cyrkle
3."No Matter What Shape (Your Stomach's In)" T Bones
4."Ballad of the Green Berets" Ssgt. Barry Sadler
5."Sloop John B" Beach Boys
6."Sunshine Superman" Donovan
7."Daydream" Lovin' Spoonful
8."Winchester Cathedral" New Vaudeville Band
9."Cherish" The Association
10."Last Train to Clarksville" Monkees
and here is 1965...
1."The Name Game" - Shirley Ellis
2."A Lover's Concerto" - The Toys
3."This Diamond Ring" - Gary Lewis & the Playboys
4."Help Me, Rhonda" - Beach Boys
5."You've Lost That Lovin' Feelin'" - The Righteous Brothers
6."Wooly Bully" - Sam the Sham & the Pharaohs
7."1-2-3" - Len Barry
8."Treat Her Right" - Roy Head and The Traits
9."I Got You Babe" - Sonny & Cher
10."Eve Of Destruction" - Barry McGuire
This may help...
Happy Listening!