The answer depends on whether you plan to use the whole sample or weigh some out.

If you plan to use the whole sample of 5.3 mg, you can calculate the number of units: 5.3 mg x 374 U/mg = 1982 units. If you were to dissolve this at 0.28 U/ml, you would end up with 1982 U/(0.28 U/ml) = 7078 ml. So instead, you would make, for example, a 1000X concentrated stock solution of 7.078 ml, or even a 10,000X stock solution of 708 µl. This could be stored as small aliquots in the freezer and diluted as needed.

If you have access to an analytical balance capable of accurately weighing out 1 mg, you could use a portion of the sample. For example, starting with 1.0 mg, you would dissolve it in (1/5.3) x 7.078 ml = 1336 µl for a 1000X solution or 134 µl for a 10,000X solution.

You should dissolve it in a suitable buffer to retain its activity.