Digging deeper into the dense Galactic globular cluster Terzan 5 with electron-multiplying CCDs. Variable star detection and new discoveries

High frame-rate imaging was employed to mitigate the effects of atmospheric turbulence (seeing) in observations of globular cluster Terzan 5. High-precision time-series photometry with the highest angular resolution so far has been obtained for the crowded central region of Terzan 5. Observations were carried out using ground-based telescopes, implementing ways to avoid saturation of the brightest stars in the field observed. The Electron-Multiplying Charge Coupled Device (EMCCD) camera installed at the Danish 1.54m telescope at the ESO La Silla Observatory was used to produce thousands of short-exposure time images (ten images per second), which were stacked to produce the normal-exposure-time images (minutes). We employed difference image analysis in the stacked images to produce high-precision photometry using the DanDIA pipeline. We analyzed the light curves of 1670 stars with 242 epochs in the crowded central region of Terzan 5 in order to statistically detect variable stars in the field observed. We present a possible visual counterpart outburst at the position of the pulsar J1748-2446N, and the visual counterpart light curve of the low-mass X-ray binary CX 3. Additionally, we present the discovery of four semiregular variables. We also present updated ephemerides and properties of the only RR Lyrae star previously known in the field covered by our observations in Terzan 5. Finally, we report a significant displacement of two sources by $ and $0.59$ arcseconds with respect to their positions in previous images available in the literature.