5. (An old entertaining problem). Divide 46 rubles into 8 parts so that each part is 50 kopecks (50 cents) more than the previous one.
5. First method of solution. Let the first part be $x$, then the second is $x+50$, the third is $-x+50 \times 2$, the fourth is $-x+50 \times 3$, the fifth is $x+50 \times 4$, the sixth is $-x+50 \times 5$, the seventh is $-x+50 \times 6$, and the eighth is $x+50 \times 7$. We will calculate the sum of all parts.

$$
\begin{gathered}
x+x+50+x+50 \times 2+x+50 \times 3+x+50 \times 4+ \\
x+50 \times 5+x+50 \times 6+x+50 \times 7= \\
=8 x+50 \times 28=8 x+1400 .
\end{gathered}
$$

Since 1400 kopecks is equal to 14 rubles, we get $8 x+14$. According to the problem, this sum is equal to 46 rubles.

We get the equation

$$
8 x+14=46,8 x=32, x=4
$$

The first part is 4 rubles, the second is 4 rubles 50 kopecks (4 rubles + 50 kopecks = 4 rubles 50 kopecks), the third is 5 rubles, the fourth is 5 rubles 50 kopecks, the fifth is 6 rubles, the sixth is 6 rubles 50 kopecks, the seventh is 7 rubles, and the eighth is 7 rubles 50 kopecks.

Second method of solution. The problem can be solved using a brief record of the problem's condition in the form of a diagram.

1) $50 \times 28=1400$ kopecks - was more than if all parts were like the first;
2) $4600-1400=3200$ kopecks - is the amount for eight equal parts;
3) $3200: 8=400$ kopecks $=4$ rubles - the first part.

Answer: 4 rubles, 4 rubles 50 kopecks, 5 rubles, 5 rubles 50 kopecks, 6 rubles, 6 rubles 50 kopecks, 7 rubles, 7 rubles 50 kopecks.