"yurari" means "slowly swing" or "slowly shimmer" or "slowly flicker" or "slowly shake". ex) otoko ga "yurari" to tatiagatta. 男が、"ゆらり" と立ち上がった。 the man standed up,and then his body was "slowly swing". suimen ga "yurari" to shita. 水面が"ゆらり"とした。 the surface of the water was slowly shake. ゆらりり yurariri is a coined word. I don't know why the songwriter odd "ri" after "yurari", but when I heard it , I feeled it gave mote cute impression to the word. 五月雨 is May rain or early summer rain.another name is 梅雨tsuyu. the season of gloomy weather by long rain. usualy, japanese don't use てみて after a noun. use after a verb. but sometimes, use to give special efect. てみて mean "try". ex)笑ってみてwarsttemite "try" to smile. so,even japanese cannot give you correct answer "what mean of 五月雨てみて" so this songs season is atound June( old cslender's May) maybe writer was playing on words. next word さぁ乱れて is similar pronounciation. it mean "let you lose your control"