The correct answer is $\boxed{\text{D}}$.
The initial profit sharing ratio between A and B is 5:3. This means that A gets 5 parts of the profit for every 3 parts that B gets. When C is admitted, he is given a $\frac{3}{10}$ share of the profits. This means that A, B, and C now share the profits in a ratio of 5:3:3. To express this as a fraction, we can multiply each part by $\frac{10}{3}$, which gives us a new profit sharing ratio of 50:30:30. This can also be written as 10:6:6, or 35:21:24.
Option A is incorrect because it does not take into account the new share that C is given. Option B is incorrect because it does not give C a share of the profits. Option C is incorrect because it does not give A and B equal shares of the profits.