Results are reported from a study of the variability of the x-ray and very high energy (VHE) γ -ray emission from Mrk 421 during a 10-day period of enchanced source activity at the end of 2005. The TeV data were taken from observations with the Whipple 10-m Cerenkov telescope and the soft x-ray data, from the ASM on board the RXTE orbital observatory. Light curves for this source indicated an obvious variability in the form of flares in both energy ranges. During the flares, the flux of VHE γ -rays exceeded that from the Crab nebula and correlated positively with the observed x-ray emission. The flux of VHE γ - rays varied almost linearly with the soft x-ray flux. The statistical characteristics of the variability were independent of energy and the two emission components were detected quasi-simultaneously. The observed temporal properties of the source can be interpreted in terms of the rapid acceleration of leptons in a jet using a synchrotron self-Compton model. Our studies confirm a flare activity intrinsic to this source on the scale of a day found in earlier studies.