The decline of the Roman Empire was more of a slow crumble than an instantaneous collapse- many events influenced each other and contributed to the demise of Roman culture in the West. When we talk about the fall of the Roman Empire, it's important to remember the sheer size of the territory that had come to be incorporated into the Empire. From Great Britain to North Africa to the Middle East, much of Europe (and Eurasia) became Roman not only in name but in culture. Even in the farthest reaches of the Empire, Roman goods, language, and public works were a vital part of shaping Roman identity in these lands. Unfortunately, the Empire and its power had become spread so thin that by the 5th century CE, Rome could no longer recover from the following conflicts.
One of the major factors, beyond a dispersal and weakening of power, was repeated invasion by "Barbarian" tribes from the North. Germanic tribes like the Vandals and the Goths invaded, raided, and dealt heavy blows to Roman cities and towns. In 410 CE, Alaric and his Visigothic tribes sacked the city of Rome, and in its weakened state was unable to prevent further attacks. In 476 CE, the Emperor Romulus Augustulus was deposed by the barbarian Odoacer, and most historians hold this date as the "end" of the Western Roman Empire.
Further compounding invasions by barbarian tribes were the weakened infrastructure and military troops. Rome sought to have troops throughout the entire Empire, especially in places where invasions occurred. Again, the size of the Roman Empire made this a challenge, and it became very expensive to maintain troops throughout the entire land. Military spending was so high that other areas, like infrastructure, suffered. Public works like roads fell into disrepair, causing trade networks and military upkeep to suffer.
In sum, the Roman Empire had grown too big too fast and was unable to maintain and defend itself.