We present observations of the Type Ia supernovae ( SNe ) 1999M , 1999N , 1999Q , 1999S , and 1999U , at redshift z \approx 0.5 . They were discovered in early 1999 with the 4.0 m Blanco telescope at Cerro Tololo Inter-American Observatory by the High- z Supernova Search Team ( HZT ) and subsequently followed with many ground-based telescopes . SNe 1999Q and 1999U were also observed with the Hubble Space Telescope . We computed luminosity distances to the new SNe using two methods , and added them to the high- z Hubble diagram that the HZT has been constructing since 1995 . The new distance moduli confirm the results of previous work . At z \approx 0.5 , luminosity distances are larger than those expected for an empty universe , implying that a “ Cosmological Constant , ” or another form of “ dark energy , ” has been increasing the expansion rate of the Universe during the last few billion years . Combining these new HZT SNe Ia with our previous results and assuming a \Lambda CDM cosmology , we estimate the cosmological parameters that best fit our measurements . For a sample of 75 low-redshift and 47 high-redshift SNe Ia with MLCS2k2 ( Jha et al . 2005 ) luminosity calibration we obtain \Omega _ { M } = 0.79 ^ { +0.15 } _ { -0.18 } and \Omega _ { \Lambda } = 1.57 ^ { +0.24 } _ { -0.32 } ( 1 \sigma uncertainties ) if no constraints are imposed , or \Omega _ { M } = 0.29 ^ { +0.06 } _ { -0.05 } if \Omega _ { M } + \Omega _ { \Lambda } = 1 is assumed . For a different sample of 58 low-redshift and 48 high-redshift SNe Ia with luminosity calibrations done using the PRES method ( a generalization of the \Delta m _ { 15 } method ) , the results are \Omega _ { M } = 0.43 ^ { +0.17 } _ { -0.19 } and \Omega _ { \Lambda } = 1.18 ^ { +0.27 } _ { -0.28 } ( 1 \sigma uncertainties ) if no constraints are imposed , or \Omega _ { M } = 0.18 ^ { +0.05 } _ { -0.04 } if \Omega _ { M } + \Omega _ { \Lambda } = 1 is assumed .