**Step 1 — Total number of outcomes.**
$$n(S) = 6 \times 6 = 36$$

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**(i) Sum of the numbers is 5**

**Step 2 — List the favourable outcomes.**
$$(1,4),\ (2,3),\ (3,2),\ (4,1)$$
$$n(E_1) = 4$$

**Step 3 — Compute the probability.**
$$P(E_1) = \frac{4}{36} = \frac{1}{9}$$

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**(ii) Difference of the numbers is 3**

**Step 4 — List the favourable outcomes.**
$$(1,4),\ (4,1),\ (2,5),\ (5,2),\ (3,6),\ (6,3)$$
$$n(E_2) = 6$$

**Step 5 — Compute the probability.**
$$P(E_2) = \frac{6}{36} = \frac{1}{6}$$

$$\boxed{\text{(i) } \frac19 \qquad \text{(ii) } \frac16}$$