A gift to a charity such as you describe is not “illegal.”  It is simply not deductible as a charitable contribution when made for the benefit of a specified individual.  The church may use it to pay the pastor’s salary and the pastor will have to declare it as income for his own tax purposes.  The church should not be giving a donation letter because it is not a deductible donation.  The church and the donor could get in trouble with the IRS if the donor sought to deduct the $5,000, but the transaction itself is not illegal.

You could probably make it a deductible contribution, however, by making the gift to pay salaries of church employees, particularly if the church has multiple employees.  The church would determine how much to pay the pastor and whether to substitute this gift for other money already in the budget for the pastor and other employees.  As long as an earmark is not set by agreement or a wink and a nod, if the church is making the decision, the gift should be deductible.