Spiral Sudoku

Suppose we have a 5×5 grid with 15 circled positions in a spiral shape as shown above. Is it possible to fill the grid with the digits 1 up to 5 in such a way that (a) each row and each column contains each digit precisely once, and (b) the circled digits include precisely one 1, two 2s, three 3s, four 4s, and five 5s? Although the short answer is “yes”…