(Abridged) We describe Spitzer IRAC and MIPS observations of the populous, 5 Myr-old open cluster NGC 2362. Early/intermediate-type confirmed/candidate cluster members either have photospheric mid-IR emission or weak, optically-thin infrared excess emission at < 24 microns consistent with debris disks. Few late-type, solar/subsolar-mass stars have primordial disks. The disk population around late-type stars is dominated by disks with inner holes (canonical transition disks) and homologously depleted disks. Both types of disks represent an intermediate stage between primordial disks and debris disks. Thus, we find that multiple paths for the primordial-to-debris disk transition exist. Our results undermine standard arguments in favor of a ~ 0.01 Myr year timescale for the transition based on data from Taurus-Auriga and rule out standard UV photoevaporation scenarios as the primary mechanism to explain the transition. Combining our data with other Spitzer surveys, we investigate the evolution of debris disks around high/intermediate-mass stars and investigate timescales for giant planet formation. If the gas and dust in disks evolve on similar timescales, the formation timescale for gas giant planets surrounding early-type, high/intermediate-mass stars is likely 1--5 Myr. Most solar/subsolar-mass stars detected by Spitzer have SEDs that indicate their disks may be actively leaving the primordial disk phase. Thus, gas giant planet formation may also occur by 5 Myr around solar/subsolar-mass stars as well.
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