
Firstly the young pup should be with his mom not strolling round the park.
I doubt very much if he's had any jabs, most vets won't vaccinate until 7/8 weeks, some vets will now vaccinate at 6 weeks, but certainly no vet would do it any earlier.
Even if he'd been vaccinated, he shouldn't be walking in the park, on or off a lead - (you couldn't walk a 5 week old pup on a lead anyway)
A lot of adult dogs & bitches find very young pups intimidating (sp?). Sometimes when a tiny pup is introduced to an older dog, the older dog will react in an unexpected way.