We seek to prove the means, motive and opportunity of 'dropout' selected 2 ≤ z ≤ 5 galaxies for large-scale structure. Together with acquired low-z tracers, these samples would map practically every linear mode and facilitate a tomographic decomposition of the Cosmic Microwave Background (CMB) lensing kernel over an unprecedented volume. With this, one may infer (the time evolution of) matter density fluctuations and perform compelling tests of horizon-scale General Relativity, neutrino masses and Inflation - viz., curvature, running of the spectral index and a scale-dependent halo bias induced by (local) primordial non-Gaussianity. This is facilitated by the order-of-magnitude increase in sensitivity achieved by planned CMB, optical-to-near-infrared imaging and spectroscopy. Focusing on traditional color-color - rather than photometric redshift - selection, we estimate the expected completeness, contamination, and spectroscopic survey speed of tailored Lyman-break galaxy (LBG) samples. With these in hand, we forecast the potential of CMB lensing cross-correlation, 'clustering redshifts' and Redshift-Space Distortions (RSD) analyses. In particular, we estimate: the depth dependence of interlopers based on CFHTLS-Archive-Research Survey (CARS) data and propagate this to biases in cosmology; a simple relation for the dependence of the linear galaxy bias on redshift and depth; new inferences of non-linear halo bias at these redshifts using legacy data; detailed forecasts of LBG spectra as would be observed by the Dark Energy Spectroscopic Instrument, Prime Focus Spectrograph, and their successors. We further assess the relative competitiveness of these spectroscopic facilities based on an intuitive figure-of-merit and define modern equivalents to traditional color selection criteria for the Large Synoptic Survey Telescope, where necessary. We confirm these science cases to be compelling for achievable facilities in the next decade by defining a LBG sample of increasing Lyman-α equivalent width with redshift, which delivers both percent-level RSD constraints on the growth rate at high-z and measurements of CMB lensing cross-correlation at z=3 and 4 with a significance measured in the hundreds, given sufficient area overlap. Finally, we discuss the limitations of this initial exploration and provide avenues for future investigation.