Solution:

Let us rename the Five gallons basket and Three gallons basket as F and T.
Fill F completely and then pour to fill T completely. By doing this you have 2 gallons remaining in F. Pour out T entirely and then fill it with the remaining liquid from F. Now, T has 2 gallons of liquid.
Fill F fully again. Now pour the liquid to fill T which has just 1 gallons of capacity remaining. By doing this, you are left with the required 4 gallons of liquid in F.

Solution:

Cry over spilt milk.

Solution:

17/19

series is 2/1 3/4 5/7 7/10 11/13 13/16
Numerator is prime number series 2-3-5-7-11-13-17
and Denominator is +3 series 1-4-7-10-13-16-19

Solution:

After five minutes, the second friend turned around to see if anyone was there or not. At this moment, he was stabbed on back by his friend.

Solution:

I am a compass.

Because I am a compass and I help people navigate all around the world.

Solution:

To do this, he must be pushing the cork inside the bottle and then taking out the coin.

Solution:

Yes. By selling them.

Solution:

Mississippi.

(For example, One Mississippi, Two Mississippi, and Three Mississippi etc.)

Solution:

All around the houses

Solution:

17

Explanation:
You can see the center circle right?
There are 16 more circles. Probably you missed them. Just concentrate on the center circle for a moment and you will find the other 16 circles.

Thus there are a total of 17 circles in the given picture.

Solution:

There can be many ways to get the job done. You can begin with a diagonal move. We are moving the 1st to the 4th place. After that, move 6 to 1, 2 to 6, 5 to 2 and 4 to 5. And you are done.
You can start with moving 6 to 3 as well. There are many other possibilities. Go figure out for yourself.

Solution:

Augustus and Joshua play all the three sports. Stacy plays none.

This is when we have assumed that girls do not play football at all. If by any means, the school has a girl's football league, all we know is that one of the three play no sports at all and the others play all the three.

Solution:

The worth of that coin is zero. This is because the B.C. and A.D. dating system was not empowered till the year 525. So the coin is probably fake.

Solution:

It is HABIT.

Solution:

The young lady was presented with a bill which belonged to the elderly woman. She had asked the waiter to collect the bill from her daughter.

Solution:

40

Explanation:
There are a total of 40 squares.
We have 8 smallest squares. Move up a size and we have 16 more + 2 in the middle. Move up a size and we have 9 more. Move up a size and we have 4 more. Then, we have the largest square.

8 + 16 + 2 + 9 + 4 + 1 = 40.

Solution:

Stephen is your grandson.

Let us explain how:
Your Uncle's sister can be your mother or can be your aunt. But in the question, you have mentioned that we have to look for the closet relation thus, it will definitely be your mother.
Now, your mother's granddaughter can either be your daughter or your niece. Again, daughter is the closer relation.
Advancing forward, your daughter's son is without a doubt your grandson.

Solution:

He is a barber.

Solution:

Logic Matchsticks Problem can be solved as shown in image below

Solution:

It is a tricky question. But it is not a question at all. It is a statement.

What is made up of 4 letters.
Described is made up of 9 letters.
Often is made up of 5 letters.
However is made up of 7 letters.
Rarely is made up of 6 letters.