Yes, according to the theory of relativity, it is theoretically possible for a spaceship to approach the speed of light, although it becomes increasingly difficult to achieve higher velocities as the speed of light is approached.
As an object with mass accelerates, its relativistic mass increases, and more energy is required to further accelerate it. This means that as the spaceship approaches the speed of light, the amount of energy needed to increase its velocity becomes immense. At around 90% of the speed of light, the energy required to accelerate the spaceship further would be extremely high, but not infinite.
It's worth noting that as the spaceship approaches the speed of light, the effects of time dilation and length contraction become more pronounced. Time dilation causes time to pass more slowly for the spaceship relative to an observer on Earth, and length contraction causes the spaceship to appear shorter in the direction of motion. These effects have been experimentally verified and are crucial to understanding the behavior of objects traveling at high speeds.
However, even at 90% of the speed of light, the relativistic effects would still be significant. For example, time dilation would mean that less time would elapse for the occupants of the spaceship compared to an observer on Earth, so a journey that appears to take a certain duration for the travelers might be perceived as much shorter by an observer on Earth.
Achieving such high velocities is a significant technological challenge due to the enormous energy requirements, engineering constraints, and the effects of acceleration on the human body. Currently, we do not possess the technology to achieve such speeds, but scientific exploration and technological advancements may potentially open up new possibilities in the future.