We have examined 40 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 auto correlation 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 ks 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 was 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 July 2012 and April 2013 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 10 - 16 April 2013. We briefly discuss models capable of explaining these blazar emissions.