We have examined 40 Nuclear Spectroscopic Telescope Array (NuSTAR) light curves (LCs) of five TeV emitting high synchrotron peaked blazars: 1ES 0229+200, Mrk 421, Mrk 501, 1ES 1959+650, and PKS 2155−304. Four of the blazars showed intraday variability in the NuSTAR energy range of 3-79 keV. Using an autocorrelation function analysis we searched for intraday variability timescales in these LCs and found indications of several between 2.5 and 32.8 ks in eight LCs of Mrk 421, a timescale around 8.0 ks for one LC of Mrk 501, and timescales of 29.6 and 57.4 ks in two LCs of PKS 2155-304. The other two blazars' LCs do not show any evidence for intraday variability timescales shorter than the lengths of those observations; however, the data were both sparser and noisier for them. We found positive correlations with zero lag between soft (3-10 keV) and hard (10-79 keV) bands for most of the LCs, indicating that their emissions originate from the same electron population. We examined spectral variability using a hardness ratio analysis and noticed a general "harder-when-brighter" behavior. The 22 LCs of Mrk 421 observed between 2012 July and 2013 April show that this source was in a quiescent state for an extended period of time and then underwent an unprecedented double-peaked outburst while monitored on a daily basis during 2013 April 10-16. We briefly discuss models capable of explaining these blazar emissions.