Let apples = a; orange = y; pears = p; mangoes = m; bananas = b
a = 2y and p = a + y
Since a = 2y; p = 2y + y = 3y

Target question => What fraction of the total number of pieces of fruit that Ann bought were pears?
$$i.e\ fraction\ of\ pear\ =\ \frac{total\ pear}{sum\ of\ all\ fruits}$$
$$\ \frac{3y}{y+2y+3y+m+b}$$
$$Find\frac{3y}{6y+m+b}$$

Statement 1 => Ann bought a total of 18 pieces of fruit
$$i.e\ 6y+m+b=18\ \ \ and\ fraction\ of\ p\ =\frac{3y}{18}$$
y is unknown, so target question cannot be answered. Statement 1 is NOT SUFFICIENT

Statement 2 =>Ann bought 5 bananas
$$b=5\ \ and\ \ fraction\ of\ p\ =\frac{3y}{6y+m+5}$$
m and y are unknown, so target question cannot be answered and statement 2 is NOT SUFFICIENT

Combining both statements together =>
$$6y+m+b=18\ and\ b\ =\ 5$$
$$6y+m+5=18$$
$$\frac{6y}{6}=\frac{18-5-m}{6}$$
$$y=\frac{13-m}{6}$$
$$fraction\ of\ p\ =\frac{3y}{18}$$
$$where\ y=\frac{13-m}{6}$$
$$=\frac{13-m}{6}\cdot\frac{1}{18}=\frac{13-m}{6\left(18\right)}$$
The value of m still remains unknown and target question cannot be answered. Therefore, both statements combined together are NOT SUFFICIENT

Answer = E