If i am repeating what someone else has already stated, I apologize.
Personally, I believe that Matthew was written long before St. Paul's martyrdom circa 64 AD. According to The Muratorian Fragment the book of Acts was already completed prior to St. Paul's release from his first imprisonment and his journeying to Spain. Since Acts was originally written as an appendix to Luke, and even the most liberal scholars consider Luke to have been the third of the synoptic gospels (Matthew, Mark and Luke) to have been written, that dates Matthew to well within the lifetime of the apostles themselves. You can read the english translation of The Muratorian Fragment here:
www.bible-researcher.com/muratorian.html
I have heard these reasons given for a late dating of the gospels:
1. Mark was the shortest of them, so it must have been written first.
2. Mark 13:1ff. speaks of the destruction of the temple in Jerusalem, so it couldn't have been written before 70 AD, when the temple was destroyed by the romans.
The length of a gospel means nothing when there is evidence that all of the synoptic gospels were written in a certain period of time. Mark's length was in all likelihood dictated by the materials at hand when it was written. A person couldn't just walk into a store to buy ink, paper, and other items as we can today. They were considered to be luxury items in a world where the vast majority of people couldn't read or write, so they were expensive.
It also didn't take an Einstein, or even a prophet, to see in Jesus' time what would eventually occur. The romans were well-known for levelling any and all cities, towns and villages that dared to oppose their rule; a city in Galilee had already been razed within Jesus' lifetime. Couple this with the rebels who were constantly trying to throw the romans out of Judea plus the corruption in the leadership of that nation, and the logical conclusion would be that eventually the people would attempt to overthrow their roman rulers, and consequently Jerusalem would be utterly destroyed.
According to evidence itself dated close to the time of Christ, Matthew, Mark and Luke, as well as Acts, were all completed prior to 62 AD. St. Paul's epistles, as well as those of the other apostles, were also completed very early in church history. So if they had lied, or even embellished, concerning the life, death and resurrection of Jesus Christ, they would have been exposed quickly and easily.
BTW: Some ultra-liberal scholars have set an extremely late date for the gospels due to their own altering of the events which made up Jesus' lifetime. They have claimed that there was no virgin birth, there were no miracles, and there was no resurrection. Jesus had simply lived out his life, run afoul of the authorities, and been crucified like so many other Jews of his day. But in order for the gospels to be embellished so as to include all of these happenings which the scholars claim never occurred, the gospels could not have been written until at least three generations had transpired between the time that Christ sojourned among us and the gospels were written down. This would automatically 'push them back' to at least 70 AD for the start of their being written.