Navarra Hospital chief Dr Javier Sesma said the five were treated for bruises but none was in serious condition.
No one was gored in the 8 am run, which lasted 2 minutes, 27 seconds.
An Australian was gored yesterday and two Americans and a Briton were gored in the first run Tuesday.
The nationally televised run sees people racing with six bulls, each weighing some 500 kilograms, along a narrow 850-metre course from a holding pen to the city bull ring.
The bulls are killed by professional matadors in bullfights each afternoon during the festival.
The nine-day fiesta, which features 24-hour street partying, was made famous in Ernest Hemingway's 1926 novel "The Sun Also Rises" and attracts thousands of foreign tourists.
Bull runs are a traditional part of summer festivals across Spain. Dozens are injured each year, mostly in falls.
In all, 15 people have died from gorings in Pamplona since record-keeping began in 1924 for the San Fermin festival.
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