Using the New Horizons LORRI camera, we searched for satellites near five Kuiper belt objects (KBOs): four cold classicals (CCs: 2011 JY 31 , 2014 OS 393 , 2014 PN 70 , 2011 HZ 102 ) and one scattered disk object (SD: 2011 HK 103). These objects were observed at distances of 0.092-0.290 au from the New Horizons spacecraft, achieving spatial resolutions of 136-430 km (resolution is ∼2 camera pixels), much higher than possible from any other facilities. Here we report that CC 2011 JY 31 is a binary system with roughly equal brightness components, CC 2014 OS 393 is likely an equal brightness binary system, while the three other KBOs did not show any evidence of binarity. The JY 31 binary has a semi-major axis of 198.6 ± 2.9 km, an orbital inclination of 61. • 34 ± 1. • 34, and an orbital period of 1.940 ± 0.002 d. The OS 393 binary objects have an apparent separation of ∼150 km, making JY 31 and OS 393 the tightest KBO binary systems ever resolved. Both HK 103 and HZ 102 were detected with SNR≈10, and our observations rule out equal brightness binaries with separations larger than ∼430 km and ∼260 km, respectively. The spatial resolution for PN 70 was ∼200 km, but this object had SNR≈2.5-3, which limited our ability to probe its binarity. The binary frequency for the CC binaries probed in our small survey (67%, not including PN 70 ) is consistent with the high binary frequency suggested by larger surveys of CCs (Fraser et al. 2017a,b;Noll et al. 2020) and recent planetesimal formation models (Nesvorný et al. 2021), but we extend the results to smaller orbit semi-major axes and smaller objects than previously possible.