We present the results from a stellar population modeling analysis of a sample of 162 z=4.5, and 14 z=5.7 Lyman alpha emitting galaxies (LAEs) in the Bootes field, using deep Spitzer/IRAC data at 3.6 and 4.5 um from the Spitzer Lyman Alpha Survey, along with Hubble Space Telescope NICMOS and WFC3 imaging at 1.1 and 1.6 um for a subset of the LAEs. This represents one of the largest samples of high-redshift LAEs imaged with Spitzer IRAC. We find that 30/162 (19%) of the z=4.5 LAEs and 9/14 (64%) of the z=5.7 LAEs are detected at >3-sigma in at least one IRAC band. Individual z=4.5 IRAC-detected LAEs have a large range of stellar mass, from 5x10^8 to 10^11 Msol. One-third of the IRAC-detected LAEs have older stellar population ages of 100 Myr - 1 Gyr, while the remainder have ages < 100 Myr. A stacking analysis of IRAC-undetected LAEs shows this population to be primarily low mass (8 -- 20 x 10^8 Msol) and young (64 - 570 Myr). We find a correlation between stellar mass and the dust-corrected ultraviolet-based star-formation rate (SFR) similar to that at lower redshifts, in that higher mass galaxies exhibit higher SFRs. However, the z=4.5 LAE correlation is elevated 4-5 times in SFR compared to continuum-selected galaxies at similar redshifts. The exception is the most massive LAEs which have SFRs similar to galaxies at lower redshifts suggesting that they may represent a different population of galaxies than the traditional lower-mass LAEs, perhaps with a different mechanism promoting Lyman alpha photon escape.
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