Expose yourself to some music in 5/4 time. This is different from a quintuplet, but it will help you start to get used to the sound of five-note groupings. If you aren't already familiar with some music in 5/4 time, start by listening to Gustav Holst's "Mars" suite from The Planets or Howard Shore's "orc" theme music from the score to "The Lord of the Rings." If you prefer more popular selections, try Brubeck's "Take Five," the theme from "Mission: Impossible," or "Happiness Is a Warm Gun," by the Beatles.
Listen specifically to some examples of quintuplets. If you have an experienced musician friend or teacher who can play them for you, listen this way. Otherwise, listen to examples from classical music: Try the last movement of Rhespigi's "Pines of Rome" or several of the movements of Stravinsky's "Rite of Spring." You may need the help of a printed score to find where they occur (these will be available at many local college libraries).
Use a verbal device. Speak a five-syllable word, such as "indispensable" or "hippopotamus." People naturally speak these words with equal lengths given to each syllable. Say the word along with a metronome, then replace the word with syllables or numbers, such as "ta ta ta ta ta" or "one, two, three, four, five."
Practice tapping and speaking the quintuplet rhythm. Use a metronome, and start with as slow a pulse as you need. Start by tapping or saying a double triplet, then remove one of the notes and lengthen the others to fit the space. Use your fingers to help keep track, tapping all five in succession.
Avoid common quintuplet pitfalls. Make sure you aren't accidentally playing a combination of a triplet and a duple, rather than five notes of the same length. You'll know you're doing this if three of your "quintuplets" are actually faster than the other two. Your rhythm will also have a more steady, regimented feel than the tense, stretching sort of feeling that a genuine quintuplet is supposed to have.
Play the quintuplet on your instrument. If you have trouble, slow things down once again.