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Two-particle correlations with K0S, Λ/Λ¯, and charged hadrons as trigger particles in the transverse momentum range 8<pT,trig<16 GeV/c, and associated charged particles within 1<pT,assoc<8 GeV/c, are studied at mid-rapidity in pp and central Pb-Pb collisions at a centre-of-mass energy per nucleon-nucleon collision sNN−−−√=5.02 TeV with the ALICE detector at the LHC. After subtracting the contributions of the flow background, the per-trigger yields are extracted on both the near and away sides, and the ratio in Pb-Pb collisions with respect to pp collisions (IAA) is computed. The per-trigger yield in Pb-Pb collisions on the away side is strongly suppressed to the level of IAA≈0.6 for pT,assoc>3 GeV/c as expected from strong in-medium energy loss, while an enhancement develops at low pT,assoc on both the near and away sides, reaching IAA≈1.8 and 2.7 respectively. These findings are in good agreement with previous ALICE measurements from two-particle correlations triggered by neutral pions (π0-h) and charged hadrons (h-h) in Pb-Pb collisions at sNN−−−√=2.76 TeV. Moreover, the correlations with K0S mesons and Λ/Λ¯ baryons as trigger particles are compared to those of inclusive charged hadrons. The results are compared with the predictions of Monte Carlo models.