  We study five-dimensional ${\cal N}=1$ Superconformal Field Theories of the
linear quiver type. These are deformed by a relevant operator, corresponding to
a homogeneous mass term for certain matter fields. The free energy is
calculated at arbitrary values of the mass parameter. After a careful
regularisation procedure, the result can be put in correspondence with a
calculation in the supergravity dual background. The F-theorem is verified for
these flows, both in field theory and in supergravity. This letter presents
some of the results in the companion paper arXiv:2211.13240.
