Question
What type of pine trees have the needles that are in bunches of 5.

Answer
Soft pines have these features:

needles usually in bundles of 5, sometimes 4.

Example

(great basin) bristlecone pine (Pinus longaeva),
Needles in bundles of 5; 1.5" long; remain on the tree over 12 years. Cones to 3" long; cone scales "bristle" with long, stiff, incurved prickles at the tips of the cone scales.
An alpine tree, growing at 10,000 to 11,500 feet, especially near the summits of the White and Inyo Mountains, in challenging climate with a short growing season. Grows slowly; may reach 20 to 60 feet tall, and up to 2 feet diameter.

foxtail pine (Pinus balfouriana),
Needles in bundles of 5; 1.5" long; remain on the branches for a decade, giving a bushy ("foxtail") appearance. Cones 3" to 5" long; scales tipped with small curved prickles.
Grows at high elevations in poor rocky soil. Two major populations exist, separated by 300 miles. The southern population grows in Kings Canyon and Sequoia National Parks, in the Sierra Nevada, 9000 to 11,300 feet; often windblown and contorted. The northern populations are in the Klamath ranges, at 6000 to 8000 feet; often erect to 50 feet tall.

limber pine (Pinus flexilis).
Needles in bundles of 5. Large cylindrical cones to 8" long. A small, short-limbed, twisted tree that grows at high elevations. The flexible (flexilis) wood is adapted to cope with snow and ice.
Grows from 8000 feet to treeline (up to 11,500 feet). Often windblown and contorted; in shelter reaches 50 feet tall.

sugar pine (Pinus lambertiana).
Needles in bundles of 5, usually twisted, with thin white lines. The longest cone of any American conifer, the mature cone is usually 16" long, but can reach 26". Reaches 200 feet tall (the tallest American pine) and 5 feet in diameter.
Common in Sierra Nevada. Found in Klamath Ranges, near sea level. Found to 9800 feet in the San Gabriel Mountains.

western white pine (Pinus monticola).
Needles in bundles of 5; to 5"; soft and flexible. Skinny cones to 8" long, typically, though sometimes to 15"; on a half-inch stalk. Botanist David Douglas first identified western white pine on Mount St. Helen's; monticola means "inhabiting mountains."
In Sierra Nevada from 7500 to 10,000 feet. Found in the Klamath Range, sometimes as low as 400 feet.

whitebark pine (Pinus albicaulis).
Needles in bundles of 5; 1" to 2.5" long; bluish-green. Almost spherical cones, to 2.5" long; mature cones disintegrate on the tree (unlike cones of other pines). In reference to the white bark noticeable on young trees, albicaulis means the "pine with white stems."
An alpine tree that grows at 10,000 feet or higher in California. Can grow to 60 feet tall, 2 feet diameter; but stunted on exposed and rocky terrain.