Pablo A. Peña, James S. Jenkins, Fabo Feng, Douglas R. Alves, Florence de Almeida, Frédéric Dux, Guang-Yao Xiao, Joanne M. Rojas M., Jose I. Vines, Rafael I. Rubenstein, R. Ramírez Reyes, Suman Saha, Connor J. Cheverall, Matías R. Díaz

The population of long-period giant planets shapes planetary system architectures and formation pathways, but these cold Jupiters remain relatively unexplored. Radial velocity (RV) surveys lose sensitivity at multi-AU separations, while transit surveys have poor detection probability at long periods. Absolute astrometry from the Hipparcos and Gaia missions offer an additional source for stellar motion that can break the orbital inclination degeneracy and strengthen detection confidence. This is especially timely ahead Gaia DR4/DR5, expected to enable routine astrometric vetting and true-mass measurements for long-period RV planets. Extending the Chile-Hertfordshire ExoPlanet Survey (CHEPS) by combining RVs spanning up to 16 years with absolute astrometry, we search for and characterise cold giants around metal-rich FGK stars. We upgrade the EMPEROR framework, incorporating astrometric differencing to jointly fit RVs and astrometry for five CHEPS targets, performing Bayesian model comparison and quantify the astrometric contribution. Our analysis characterises orbital parameters for two known planets in HIP 21850 and detects five new: a warm Jupiter--HIP 10090c, orbital period $P=321.8 \pm 0.5$ d and mass $M=0.85 \pm 0.08$ $M_J$, and four Jupiter analogues--HIP 8923b, with $P=14.1 \pm 0.06$ yr and $M=9.98\pm 0.47 M_J$, HIP 10090b with $P=8.1\pm 0.3$ yr and $M=3.87\pm 0.63$ $M_J$, HIP 39330b with $P=12.7\pm 0.7$ yr and $M=1.68\pm 0.15$ $M_J$, and HIP 98599b with $P=7.3\pm 0.1$ yr and $M=6.85\pm 0.16$ $M_J$. Adding astrometry reduces period and mass uncertainties by factors between 3 and 10 and increases the Bayes factor by up to 60. The synergy of long-baseline RVs and absolute astrometry provides a robust pathway to discover and characterise cold giant planets. Our results demonstrate that astrometry meaningfully improves detection confidence and converts minimum masses into true masses.