Of course one should try to pray within the specified times. There is wisdom in the Islamic prayer schedule, setting times throughout the day to "take a break" to remember God's blessings and to seek His guidance.
If a prayer is missed, it is common practice among Muslims that it is to be made up as soon as it is remembered or as soon as one is able to do so. This is known as Qadaa'. For example, if one misses the noon prayer because of a work meeting that could not be interrupted, one should pray as soon as the meeting is over. If the next prayer time has already come, one should first perform the prayer that was missed, and immediately after it the “on time” prayer.
It is incorrect to simply throw up one’s hands and say, “Oh, it was missed and there is nothing to do about it.” There are times when prayer is missed for unavoidable reasons. It is indeed a sin if one misses prayers regularly without a valid reason (i.e. constantly oversleeping the pre-dawn prayer). However, the door to repentance is open and the first step is to make up the missed prayer as soon as possible. One should repent any delay that was due to negligence or forgetfulness, and commit to developing the habit of performing the prayers within their timeframe.
Here are some links to scholarly opinions which support what is outlined above: