Will a Vivitar
Series One Zoom 28-300mm lens work correctly on a Minolta
Maxxum 5 Digital Camera?
Vivitar is a third-party lens maker that can make a lens in a variety of camera mounts, so there's no way anyone can answer your question without being able to see the specific lens you're talking about. I'd suggest looking through a visual guide to lens mounts to see if the Vivitar uses the mount for the Minolta AF or Sony A-mount systems (the mount the Maxxum 5 uses).
This is Minolta's autofocus mount. The manual-focus SLR mounts, (Minolta MD and Minolta MC) cannot be used directly on the Maxxum 5.
Very briefly, lenses are generally only compatible with one particular mount, so if you want a lens for a Minolta Maxxum 5D, then you need to buy an A-mount lens, which is the name of the mount used on that camera. Minolta developed the A-mount for their interchangeable-lens autofocus cameras, and Sony also uses the A-mount. (Be aware though that Sony also has interchangeable-lens cameras that use another mount called the E-mount, and E-mount lenses are not compatible with A-mount camera bodies. Also, don't confuse A-mount with Sony Alpha (α), the brand name that Sony uses to refer to its range of interchangeable-lens cameras as a whole, encompassing both A-mount and E-mount.)
You will find A-mount lenses from Sony and Minolta and also third-party lens manufacturers such as Sigma, Tamron and Tokina amongst others.