  Amongst the intermediate mass pulsating stars known as $\delta$ Sct stars is
a subset of high-amplitude and predominantly radial-mode pulsators known as
high-amplitude $\delta$ Sct (HADS) stars. From more than 2000 $\delta$ Sct
stars observed by the Kepler space mission, only two HADS stars were detected.
We investigate the more perplexing of these two HADS stars, KIC5950759. We
study its variability using ground- and space-based photometry, determine its
atmospheric parameters from spectroscopy and perform asteroseismic modelling to
constrain its mass and evolutionary stage. From spectroscopy, we find that
KIC5950759 is a metal-poor star, which is in agreement with the inferred
metallicity needed to reproduce its pulsation mode frequencies from
non-adiabatic pulsation models. Furthermore, we combine ground-based WASP and
Kepler space photometry, and measure a linear change in period of order
$\dot{P}/P \simeq 10^{-6}$ yr$^{-1}$ for both the fundamental and first
overtone radial modes across a time base of several years, which is at least
two orders of magnitude larger than predicted by evolution models, and is the
largest measured period change in a $\delta$ Sct star to date. Our analysis
indicates that KIC5950759 is a metal-poor HADS star near the short-lived
contraction phase and the terminal-age main sequence, with its sub-solar
metallicity making it a candidate SX Phe star. KIC5950759 is a unique object
amongst the thousands of known $\delta$ Sct stars and warrants further study to
ascertain why its pulsation modes are evolving remarkably faster than predicted
by stellar evolution.
