Proton captures on Mg isotopes play an important role in the Mg-Al cycle active in stellar H-burning regions. In particular, low-energy nuclear resonances in the $^{25}$Mg(p,$gamma$)$^{26}$Al reaction affect the production of radioactive $^{26}$Al$^{gs}$ as well as the resulting Mg/Al abundance ratio. Reliable estimations of these quantities require precise measurements of the strengths of low-energy resonances. Based on a new experimental study performed at LUNA, we provide revised rates of the $^{25}$Mg(p,$gamma$)$^{26}$Al$^{gs}$ and the $^{25}$Mg(p,$gamma$)$^{26}$Al$^{m}$ reactions with corresponding uncertainties. In the temperature range 50 to 150 MK, the new recommended rate of the $^{26}$Al$^{m}$ production is up to 5 times higher than previously assumed. In addition, at T$=100$ MK, the revised total reaction rate is a factor of 2 higher. Note that this is the range of temperature at which the Mg-Al cycle operates in an H-burning zone. The effects of this revision are discussed. Due to the significantly larger $^{25}$Mg(p,$gamma$)$^{26}$Al$^{m}$ rate, the estimated production of $^{26}$Al$^{gs}$ in H-burning regions is less efficient than previously obtained. As a result, the new rates should imply a smaller contribution from Wolf-Rayet stars to the galactic $^{26}$Al budget. Similarly, we show that the AGB extra-mixing scenario does not appear able to explain the most extreme values of $^{26}$Al/$^{27}$Al, i.e. $>10^{-2}$, found in some O-rich presolar grains. Finally, the substantial increase of the total reaction rate makes the hypothesis of a self-pollution by massive AGBs a more robust explanation for the Mg-Al anticorrelation observed in Globular-Cluster stars.
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