This paper investigates new constraints on f(T) gravity using recent Baryon Acoustic Oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) and Type Ia supernovae (SNeIa) data from the Dark Energy Survey Supernova Program (DES-SN5YR). The authors explore f(T) cosmological models 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) models over the standard ΛCDM model, with a derived Hubble constant (H_0) of 68.3^{+3.0}_{-3.5} [km/s/Mpc], which is in agreement with the SH0ES collaboration but with larger uncertainty. The Hubble tension, a significant discrepancy between the local measurement of H_0 from Type Ia supernovae and the value inferred from the Cosmic Microwave Background (CMB), has reached a statistical significance of ~5σ. This tension has led to the exploration of alternative cosmological models beyond the ΛCDM framework. The DESI BAO data and DES-SN5YR data suggest a preference for time-varying dark energy, and several studies have proposed various models to address this tension, including axion-inspired models, interacting dark energy models, and quintessence scalar field models. The authors consider two specific f(T) models: the power-law model (f_1) and the Linder model (f_2). They use Markov Chain Monte Carlo (MCMC) analysis to constrain these models and compare them with the ΛCDM model. The results show that the f(T) models slightly prefer a lower fractional matter density and a similar product r_d h compared to the ΛCDM model. However, the Bayes factors for both models favor the ΛCDM model, indicating that the evidence for f(T) models is not strong enough to explain the Hubble tension. The paper concludes that f(T) cosmologies, constrained by new BAO measurements from DESI 2024 and other datasets, could be a viable alternative to explain the current Hubble tension. Further analyses using upcoming data releases will be conducted to explore these extended gravity models and their potential to address the cosmological tension.This paper investigates new constraints on f(T) gravity using recent Baryon Acoustic Oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) and Type Ia supernovae (SNeIa) data from the Dark Energy Survey Supernova Program (DES-SN5YR). The authors explore f(T) cosmological models 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) models over the standard ΛCDM model, with a derived Hubble constant (H_0) of 68.3^{+3.0}_{-3.5} [km/s/Mpc], which is in agreement with the SH0ES collaboration but with larger uncertainty. The Hubble tension, a significant discrepancy between the local measurement of H_0 from Type Ia supernovae and the value inferred from the Cosmic Microwave Background (CMB), has reached a statistical significance of ~5σ. This tension has led to the exploration of alternative cosmological models beyond the ΛCDM framework. The DESI BAO data and DES-SN5YR data suggest a preference for time-varying dark energy, and several studies have proposed various models to address this tension, including axion-inspired models, interacting dark energy models, and quintessence scalar field models. The authors consider two specific f(T) models: the power-law model (f_1) and the Linder model (f_2). They use Markov Chain Monte Carlo (MCMC) analysis to constrain these models and compare them with the ΛCDM model. The results show that the f(T) models slightly prefer a lower fractional matter density and a similar product r_d h compared to the ΛCDM model. However, the Bayes factors for both models favor the ΛCDM model, indicating that the evidence for f(T) models is not strong enough to explain the Hubble tension. The paper concludes that f(T) cosmologies, constrained by new BAO measurements from DESI 2024 and other datasets, could be a viable alternative to explain the current Hubble tension. Further analyses using upcoming data releases will be conducted to explore these extended gravity models and their potential to address the cosmological tension.