  The 5:3 and 7:4 mean motion resonances of Neptune are at 42.3 and 43.7 au,
respectively, and overlap with objects in the Classical trans-neptunian belt
(Kuiper belt). We report the complete/partial lightcurves of 13 and 14
trans-Neptunian objects (TNOs) in the 5:3 and 7:4 resonances, respectively. We
report a most likely contact binary in the 7:4 resonance, 2013 FR$_{28}$, with
a periodicity of 13.97$\pm$0.04 h and a lightcurve amplitude of 0.94$\pm$0.02
mag. With a V-/U-shaped lightcurve, 2013 FR$_{28}$ has one of the largest
well-sampled TNO amplitude observed with ground-based observations, comparable
to the well-determined contact binary 2001 QG$_{298}$. 2013 FR$_{28}$ has a
mass ratio q$\sim$1 with a density $\rho$$\sim$1 g cm$^{-3}$. We find several
objects with large amplitudes and classify 2004 SC$_{60}$, 2006 CJ$_{69}$, and
2013 BN$_{82}$ as likely contact binaries, and 2001 QF$_{331}$, 2003
YW$_{179}$, and 2015 FP$_{345}$ as likely elongated objects. We observe the
17:9 resonant or classical object 2003 SP$_{317}$ that we classify as a likely
contact binary. A lower estimate of 10-50% and 20-55% for the fraction of
(nearly) equal-sized contact binaries is calculated in the 5:3 and 7:4
resonances, respectively. Surface colors of 2004 SC$_{60}$, 2013 BN$_{82}$,
2014 OL$_{394}$, and 2015 FP$_{345}$ have been obtained. Including these colors
with ones from the literature reveals that elongated objects and contact
binaries share the same ultra-red surface color, except Manw\"e-Thorondor and
2004 SC$_{60}$. Not only are the colors of the 7:4 and 5:3 TNOs similar to the
Cold Classicals, but we demonstrate that the rotational properties of the 5:3
and 7:4 resonants are similar to those of the Cold Classicals, inferring a
clear link between these sub-populations.
