Low-luminosity active galactic nuclei (AGNs) with low-mass black holes (BHs) in the early universe are fundamental to understanding the BH growth and their coevolution with the host galaxies. Utilizing JWST NIRCam Wide Field Slitless Spectroscopy, we perform a systematic search for broad-line Hα emitters (BHAEs) at z ≈ 4–5 in 25 fields of the A SPectroscopic survey of biased halos In the Reionization Era (ASPIRE) project, covering a total area of 275 arcmin$^{2}$. We identify 16 BHAEs with FWHM of the broad components spanning from ∼1000 to 3000 km s$^{−1}$. Assuming that the broad line widths arise as a result of Doppler broadening around BHs, the implied BH masses range from 10$^{7}$ to 10$^{8}$M$_{⊙}$, with broad Hα-converted bolometric luminosities of 10$^{44.5}$–10$^{45.5}$ erg s$^{−1}$ and Eddington ratios of 0.07–0.47. The spatially extended structure of the F200W stacked image may trace the stellar light from the host galaxies. The Hα luminosity function indicates an increasing AGN fraction toward the higher Hα luminosities. We find possible evidence for clustering of BHAEs: two sources are at the same redshift with a projected separation of 519 kpc; one BHAE appears as a composite system residing in an overdense region with three close companion Hα emitters. Three BHAEs exhibit blueshifted absorption troughs indicative of the presence of high column density gas. We find that the broad-line-selected and photometrically selected BHAE samples exhibit different distributions in the optical continuum slopes, which can be attributed to their different selection methods. The ASPIRE broad-line Hα sample provides a good database for future studies of faint AGN populations at high redshift.