We present results of a survey for Ly alpha emitters at z=4.86 based on optical narrowband (lambda_c=7126 angstrom, Delta lambda=73 angstrom) and broadband (B, V, r', i', and z') observations of the Cosmic Evolution Survey (COSMOS) field using Suprime-Cam on the Subaru Telescope. We find 79 LAE candidates at z=4.86 over a contiguous survey area of 1.83 deg^2, down to the Ly alpha line flux of 1.47 x 10^-17 ergs s^-1 cm^-2. We obtain the Ly alpha luminosity function with a best-fit Schechter parameters of log L^*=42.9^+0.5_-0.3 ergs s^-1 and phi^* = 1.2^+8.0_-1.1 x 10^-4 Mpc^-3 for alpha=-1.5 (fixed). The two-point correlation function for our LAE sample is xi(r) = (r/4.4^+5.7_-2.9 Mpc)^-1.90+/-0.22. In order to investigate the field-to-field variations of the properties of Ly alpha emitters, we divide the survey area into nine tiles of 0.5^circ x 0.5^circ each. We find that the number density varies with a factor of ~ 2 from field to field with high statistical significance. However, we find no significant field-to-field variance when we divide the field into four tiles with 0.7^circ x 0.7^circ each. We conclude that at least 0.5 deg^2 survey area is required to derive averaged properties of LAEs at z~5, and our survey field is wide enough to overcome the cosmic variance.