This study investigates the constraints on $ f(T) $ gravity using the latest Baryon Acoustic Oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) and the Type Ia supernovae (SNIa) catalog from the Dark Energy Survey Supernova Program (DES-SN5YR). The $ f(T) $ gravity models considered are characterized by power law late-time accelerated expansion. The combination of DESI BAO and $ r_d $ CMB Planck data suggests a Bayesian preference for $ f(T) $ cosmological models over the $ \Lambda $ CDM model, yielding a $ H_0 = 68.3_{-3.5}^{+3.0} $ [km/s/Mpc], consistent with the SH0ES collaboration, though with larger uncertainties. The Hubble tension, with a statistical significance of $ \sim5\sigma $, highlights a discrepancy between the local distance ladder method's $ H_0 = 73 \pm 1 $ [km/s/Mpc] and the CMB-based $ H_0 = 67.4 \pm 0.5 $ [km/s/Mpc]. This tension has prompted exploration of alternative cosmological models. Recent BAO measurements from DESI and SNIa from DES-SN5YR suggest a $ 2\sigma $ preference for time-varying dark energy. Various models, including axion-early dark energy, interacting dark energy, quintessence scalar field, and thermodynamics-inspired dark energy models, have been studied to address the Hubble tension. The study presents results for two $ f(T) $ models: the power law model $ f_1(T) $ and the Linder model $ f_2(T) $. The power law model $ f_1(T) $, defined as $ f_1(T) = (-T)^{p_1} $, shows a slight preference over $ \Lambda $ CDM, with a Bayes factor of $ \ln \mathcal{B}_{ij} = +1.34 $. The Linder model $ f_2(T) $, defined as $ f_2(T) = T_0(1 - e^{-p_2\sqrt{T/T_0}}) $, also shows a slight preference, with a Bayes factor of $ \ln \mathcal{B}_{ij} = +0.33 $. The study uses MCMC analysis with emcee and GetDist to test these models against the data. The results show that the $ f(T) $ models provide a slight Bayesian preference over $ \Lambda $ CDM, though the evidence is not strong. The inclusion of $ r_d $ prior from Planck, BBN, or other datasets helps alleviate the Hubble tension. The study concludes that $ f(T) $ cosmologiesThis study investigates the constraints on $ f(T) $ gravity using the latest Baryon Acoustic Oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) and the Type Ia supernovae (SNIa) catalog from the Dark Energy Survey Supernova Program (DES-SN5YR). The $ f(T) $ gravity models considered are characterized by power law late-time accelerated expansion. The combination of DESI BAO and $ r_d $ CMB Planck data suggests a Bayesian preference for $ f(T) $ cosmological models over the $ \Lambda $ CDM model, yielding a $ H_0 = 68.3_{-3.5}^{+3.0} $ [km/s/Mpc], consistent with the SH0ES collaboration, though with larger uncertainties. The Hubble tension, with a statistical significance of $ \sim5\sigma $, highlights a discrepancy between the local distance ladder method's $ H_0 = 73 \pm 1 $ [km/s/Mpc] and the CMB-based $ H_0 = 67.4 \pm 0.5 $ [km/s/Mpc]. This tension has prompted exploration of alternative cosmological models. Recent BAO measurements from DESI and SNIa from DES-SN5YR suggest a $ 2\sigma $ preference for time-varying dark energy. Various models, including axion-early dark energy, interacting dark energy, quintessence scalar field, and thermodynamics-inspired dark energy models, have been studied to address the Hubble tension. The study presents results for two $ f(T) $ models: the power law model $ f_1(T) $ and the Linder model $ f_2(T) $. The power law model $ f_1(T) $, defined as $ f_1(T) = (-T)^{p_1} $, shows a slight preference over $ \Lambda $ CDM, with a Bayes factor of $ \ln \mathcal{B}_{ij} = +1.34 $. The Linder model $ f_2(T) $, defined as $ f_2(T) = T_0(1 - e^{-p_2\sqrt{T/T_0}}) $, also shows a slight preference, with a Bayes factor of $ \ln \mathcal{B}_{ij} = +0.33 $. The study uses MCMC analysis with emcee and GetDist to test these models against the data. The results show that the $ f(T) $ models provide a slight Bayesian preference over $ \Lambda $ CDM, though the evidence is not strong. The inclusion of $ r_d $ prior from Planck, BBN, or other datasets helps alleviate the Hubble tension. The study concludes that $ f(T) $ cosmologies