Given U1 = 5 and the recursive formula Un+1 = 3 + (1)/(4) Un, calculate the terms U2, U3, and U4.

We use the formula $U_{n+1} = 3 + \frac{1}{4} U_n$ with $n=1$.

$$U_2 = 3 + \frac{1}{4} U_1$$

Substitute $U_1 = 5$:

$$U_2 = 3 + \frac{1}{4} (5)$$ $$U_2 = 3 + \frac{5}{4}$$ $$U_2 = \frac{12}{4} + \frac{5}{4}$$ $$U_2 = \frac{17}{4}$$

We use the formula $U_{n+1} = 3 + \frac{1}{4} U_n$ with $n=2$.

$$U_3 = 3 + \frac{1}{4} U_2$$

Substitute $U_2 = \frac{17}{4}$:

$$U_3 = 3 + \frac{1}{4} \left(\frac{17}{4}\right)$$ $$U_3 = 3 + \frac{17}{16}$$ $$U_3 = \frac{48}{16} + \frac{17}{16}$$ $$U_3 = \frac{65}{16}$$

We use the formula $U_{n+1} = 3 + \frac{1}{4} U_n$ with $n=3$.

$$U_4 = 3 + \frac{1}{4} U_3$$

Substitute $U_3 = \frac{65}{16}$:

$$U_4 = 3 + \frac{1}{4} \left(\frac{65}{16}\right)$$ $$U_4 = 3 + \frac{65}{64}$$ $$U_4 = \frac{192}{64} + \frac{65}{64}$$ $$U_4 = \frac{257}{64}$$

The terms are:
$U_2 = \boxed{\frac{17}{4}}$
$U_3 = \boxed{\frac{65}{16}}$
$U_4 = \boxed{\frac{257}{64}}$