  Terzan 5 is a complex stellar system in the Galactic bulge, harboring stellar
populations with very different iron content ({\Delta}[Fe/H] ~1 dex) and with
ages differing by several Gyrs. Here we present an investigation of its
variable stars. We report on the discovery and characterization of three RR
Lyrae stars. For these newly discovered RR Lyrae and for six Miras of known
periods we provide radial velocity and chemical abundances from spectra
acquired with X-SHOOTER at the VLT. We find that the three RR Lyrae and the
three short period Miras (P<300 d) have radial velocity consistent with being
Terzan 5 members. They have sub-solar iron abundances and enhanced
[{\alpha}/Fe], well matching the age and abundance patterns of the 12 Gyr
metal-poor stellar populations of Terzan 5. Only one, out of the three long
period (P>300 d) Miras analyzed in this study, has a radial velocity consistent
with being Terzan 5 member. Its super-solar iron abundance and solar-scaled
[{\alpha}/Fe] nicely match the chemical properties of the metal rich stellar
population of Terzan 5 and its derived mass nicely agrees with being several
Gyrs younger than the short period Miras. This young variable is an additional
proof of the surprising young sub-population discovered in Terzan 5.
