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 and provide only minimum planet masses, 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 framework, incorporating astrometric differencing to jointly fit RVs and astrometry for five CHEPS targets, performing Bayesian model comparison and baseline- and phase-coverage metrics to quantify the astrometric contribution. Our analysis confirms and characterises orbital parameters for two known planets in HIP 21850 and detects five new planets: a warm Jupiter -- HIP 10090c, with orbital period P=321.8^+0.3^-0.6_d and mass M=0.85^+0.03^-0.12_M_J_, and four Jupiter analogues -- HIP 8923b with P=14.1^+0.4^-0.7_yr and M=9.98^+0.78^-0.16_M_J_, HIP 10090b with P=8.1^+0.3^-0.3_yr and M=3.87^+0.65^-0.60_M_J_, HIP 39330b with P=12.7^+0.6^-0.7_yr and M=1.68^+0.16^-0.13_M_J_, and HIP 98599b with P=7.3^+0.1^-0.1_yr and M=6.85^+0.10^-0.22_M_J_. Adding astrometry reduces period and mass uncertainties by factors between 3 and 10, whilst increasing the Bayes' factors by up to ~60. The synergy of long-baseline RVs and absolute astrometry provides a robust pathway to discover and characterise cold giant planets and metal-rich Solar-System analogues. Our results demonstrate that astrometric samples meaningfully improve detection confidence and convert minimum masses into true masses. This approach fills the demographic gap between RV and direct imaging sensitivities and prepares the field for forthcoming astrometric missions that will allow to find stellar systems like our own.

Cone search capability for table J/A+A/709/A213/stars (List of studied stars)