To solve the proportion 1/x : 1/3 = 1/2 : 1/5, we can cross-multiply.

Cross-multiplying gives us (1/x)(1/5) = (1/3)(1/2).

Simplifying both sides, we have 1/(5x) = 1/6.

To solve for x, we can take the reciprocal of both sides.

Reciprocating both sides gives us 5x = 6.

Finally, we can solve for x by dividing both sides by 5.

Dividing both sides by 5 gives us x = 6/5.

Therefore, the value of x in the given proportion is x = 6/5.