A person and go on a mission at any age from 19 (21 for women) and up. The primary requirements for mission service are to be a faithful member of the church, be healthy enough to do the work, have a desire to serve, and have the financial resources to support yourself while serving. This last requirement is why you don't see many middle-aged missionaries. People in that age range are usually too busy raising families and making a living. They really don't have the time to devote to full-time missionary service. However, if you are wealthy enough that you don't need to work for a living and don't have children that are dependent on you, then I don't see why you can't serve a mission if you desire to do so.

The Church Handbook of Instructions states the following: "Church leaders should encourage all worthy, able, single men ages 19 through 25 to serve full-time missions. Full-time missionary service is a priesthood responsibility of these young men. They are called to serve for 24 months. "In some instances, single men ages 26 and older may be called to serve locally in nonproselyting assignments. "Bishops and stake presidents should prayerfully consider which couples in their units could be called to serve as full-time missionaries. Bishops may interview them to determine availability, ask them to prepare for a full-time mission call, and help them complete and submit the recommendation forms. "Couples normally serve for 12, 18, or 24 months. A 6-month term of service will be considered only for those in special situations such as agricultural occupations. Couples serving outside their native land are called for at least 18 months. Assignments for couples are outlined on page 88. "Couples who are recommended for full-time missionary service must no longer be engaged in full-time employment. If the couple will be serving away from home, they must not have any dependent children living at home. Bishops and stake presidents should take special care to ensure that couples are in good enough health to serve effectively as full-time missionaries." To answer your question, it depends on what you mean by 'mission'. A 50-year-old single man cannot serve a full-time proselytising mission (the kind most think fo when referrign to a mission). A 50-year-old married man can if he is no longer employed and his children are moved away from home. A 50-year-old man, single or married, can server a non-proselytising mission locally.