The programs that the impressive New York Youth Symphony presents at Carnegie Hall are typically ambitious and substantive. So it was on Sunday afternoon, when the orchestra played its final concert of the season, the last to be conducted by Ryan McAdams, who has ended his five-year tenure as music director. The main work was Mahler’s Symphony No. 5 in C sharp minor, a complex, craggy and demanding score lasting some 75 minutes. And Mr. McAdams drew an energetic and involving performance from the inspired players, who range in age from 12 to 22.


Every program this ensemble gives at Carnegie Hall includes the premiere of a work written by a young composer. This one had “On the Hunt,” a restless, fitful 15-minute piece for horn quartet and orchestra by Elizabeth A. Kelly.


But after Ms. Kelly’s piece, before intermission, these young players revealed a sentimental side, when they played an unscheduled piece in tribute to Mr. McAdams: an arrangement for violin and orchestra of the aria “O mio babbino caro” from Puccini’s “Gianni Schicchi,” with the concertmaster Samuel Katz as soloist, and Sarah Kidd, the assistant conductor, taking over the podium. The aria has one of those Puccini tunes that grab you. Mr. Katz played it with lovely sound and lyricism. Mr. McAdams, standing in front of the players as he listened, seemed overcome.


In introducing the tribute performance, Leslie J. Garfield, the chairman of the orchestra’s board, said that the New York Youth Symphony had an admirable history of choosing rising young music directors who go on to have notable careers. This was no idle boast. You need only look down the list of 15 conductors to date: names like Leonard Slatkin, Myung-Whun Chung and Miguel Harth-Bedoya. Paul Haas, Mr. McAdams’s immediate predecessor, who is also a composer, has appeared with the Orchestra of St. Luke’s, the National Symphony, the New World Symphony and others.


Mr. McAdams’s career started taking off while he was with the New York Youth Symphony. He has conducted regularly with the New York City Ballet and has appeared with the Israel Philharmonic, the Los Angeles Philharmonic, the St. Paul Chamber Orchestra and Maggio Musicale in Florence. He proved himself again on Sunday, starting with the new piece by Ms. Kelly, who is completing a Ph.D. in composition at the Eastman School of Music.


In “On the Hunt” she evokes, transforms and distorts the musical associations of horn calls with hunting and the Romantic hero. The solo parts were played by a horn quartet of four women with the irreverent name Genghis Barbie. The ensemble has won fans through its arrangements of pop, rock, jazz, indie and classical contemporary music. It dispatched the demands of Ms. Kelly’s piece with aplomb and vitality.


The work begins with quizzical solo horn calls that soon overlap into disjointed phrases. Gradually the orchestra surrounds the quartet with ambiguous string harmonies, anxious blasts and warbling woodwinds, culminating in a frenetic chase to the growling conclusion of this deconstructed hunting music.


After intermission these intrepid players took on Mahler’s Fifth. Without a strongly shaped, clearly executed performance, this symphony can easily seem baffling. The New York Youth Symphony’s sound may not have had the polish of a professional orchestra, but Mr. McAdams drew vivid, colorful and often incisive playing from the young musicians. The scherzo is driven by a solo horn part, and in this performance the excellent principal horn player, Nathanael Udell, stood in front of the orchestra like a concerto soloist, which allowed the role of the horn to come through the whole with enhanced drama. The finale balanced episodes of hurtling power with passages of delicacy and grace.


The ovation went on and on as Mr. McAdams singled out players for bows and accepted many hugs. His successor, Joshua Gersen, will make his Carnegie Hall debut in November, when he conducts the orchestra in its 50th-anniversary concert.