The number of petals a flower has can be an important key to identifying the flower. Newcombe's Wildflower Guide is based on this concept.
An important thing to remember about this concept is that the "number of petals" represents the number of apparent petals. This is not necessarily the botanically-correct number of petals. Oftentimes what appear to be petals are actually sepals or bracts. It is an aid to identification, not a botanical classification.

Apple, Common (Malus pumila)
Arrowwood, Downy (Viburnum rafinesquianum)
Arrowwood, Smooth (Viburnum recognitum)
Baked-apple Berry (Rubus chamaemorus)
Bearberry (Arctostaphylos uva-ursi)
Bladdernut (Staphylea trifolia)
Blueberry, Velvetleaf (Vaccinium myrtilloides)
Buckthorn, Alder-leaved (Rhamnus alnifolia)
Cherry, Sand (Prunus pumila)
Chokeberry (Aronia melanocarpa)
Chokecherry (Prunus virginiana)
Cinquefoil, Shrubby (Dasiphora fruticosa)
Cinquefoil, Three-toothed (Sibbaldia tridentata)
Creeper, Trumpet (Campsis radicans)
Currant, Northern Wild Black (Ribes hudsonianum)
Currant, Wild Black (Ribes americanum)
Elderberry, Common (Sambucus nigra)
Elderberry, Red-berried (Sambucus racemosa)
Gooseberry, Prickly (Ribes cynosbati)
Gooseberry, Wild (Ribes hirtellum)
Hercules' Club (Aralia elata)
Hobblebush (Viburnum lantanoides)
Honeysuckle, American Fly (Lonicera canadensis)
Honeysuckle, Bush (Diervilla lonicera)
Ivy, Poison (Toxicodendron rydbergii)
Juneberry, Mountain (Amelanchier bartramiana)
Leatherleaf (Chamaedaphne calyculata)
Nannyberry (Viburnum lentago)
Pipsissewa (Chimaphila umbellata)
Plum, Canada (Prunus nigra)
Raisin, Wild (Viburnum nudum)
Raspberry, Wild Red (Rubus idaeus)
Rose, Prairie (Rosa setigera)
Rose, Prickly Wild (Rosa acicularis)
Rose, Swamp (Rosa palustris)
Serviceberry, Downy (Amelanchier arborea)
Serviceberry, Low (Amelanchier humilis)
Serviceberry, Smooth (Amelanchier laevis)
Serviceberry, Swamp (Amelanchier canadensis)
St Johnswort, Kalm's (Hypericum kalmianum)
St Johnswort, Shrubby (Hypericum prolificum)
Sumac, Fragrant (Rhus aromatica)
Sumac, Poison (Toxicodendron vernix)
Twinflower (Linnaea borealis)
Wintergreen (Gaultheria procumbens)

Irregular 2 petals 3 petals 4 petals 5 petals 6 petals 7 or more Indistinguishable

THUMBNAILS
Apple, Common (Malus pumila)	Arrowwood, Smooth (Viburnum recognitum)	Baked-apple Berry (Rubus chamaemorus)	Bearberry (Arctostaphylos uva-ursi)

Bladdernut (Staphylea trifolia)	Currant, Northern Wild Black (Ribes hudsonianum)	Elderberry, Common (Sambucus nigra)	Elderberry, Red-berried (Sambucus racemosa)

Hercules' Club (Aralia elata)	Juneberry, Mountain (Amelanchier bartramiana)	Leatherleaf (Chamaedaphne calyculata)	Pipsissewa (Chimaphila umbellata)

Plum, Canada (Prunus nigra)	Raspberry, Wild Red (Rubus idaeus)	Rose, Prairie (Rosa setigera)	Rose, Prickly Wild (Rosa acicularis)

Rose, Swamp (Rosa palustris)	Serviceberry, Downy (Amelanchier arborea)	Serviceberry, Low (Amelanchier humilis)	Serviceberry, Smooth (Amelanchier laevis)

Serviceberry, Swamp (Amelanchier canadensis)	St Johnswort, Shrubby (Hypericum prolificum)	Twinflower (Linnaea borealis)	Wintergreen (Gaultheria procumbens)

Irregular 2 petals 3 petals 4 petals 5 petals 6 petals 7 or more Indistinguishable

To see all Species with 5 Flower Parts in order by Common Name → START HERE