We have determined the mass-density radial profiles of the first five strong gravitational lens systems discovered by the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS). We present an enhancement of the semi-linear lens inversion method of Warren & Dye which allows simultaneous reconstruction of several different wavebands and apply this to dual-band imaging of the lenses acquired with the Hubble Space Telescope. The five systems analysed here have lens redshifts which span a range, 0.22<z<0.94. Our findings are consistent with other studies by concluding that: 1) the logarithmic slope of the total mass density profile steepens with decreasing redshift; 2) the slope is positively correlated with the average total projected mass density of the lens contained within half the effective radius and negatively correlated with the effective radius; 3) the fraction of dark matter contained within half the effective radius increases with increasing effective radius and increases with redshift.