First of all Charlie, I presume your diagrams are correct and the thread title should be 2-5. (2-4 is another possible approach). The idea with both of these low approaches is indeed to settle more easily on the side. Compared to the usual knight's move approach they are lower, so are not commonly seen against an isolated 4-4 point. You most often seem them against a 4-4 plus an extra stone as then the usual approach doesn't work so well:
- Click Here To Show Diagram Code
[go]$$Wc Normal approach not so good
$$ -----------------+
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . B . . . . . |
$$ . . . a X . . . |
$$ . . . . . 2 . . |
$$ . . . . 3 1 . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . 4 . . . |
$$ . . . . , . . . |
$$ . . . . . . . . |[/go]
As black already has the extra marked stone, after kicking at r15 (to stop, in sente, white sliding to s16) he can make a pincer to attack white as he doesn't need to spend a move to reinforce against white a. Of course this diagram is not always bad for white, for example if white thickness below 4 means 4 is a weaker group than 1&3 it could be playable, and there is still 3-3 aji, but usually the two heavy white stones are a problem.
- Click Here To Show Diagram Code
[go]$$Wc Low approach better
$$ -----------------+
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . X . . . . . |
$$ . . . . X 4 2 . |
$$ . . . . . 3 1 . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . 5 . . |
$$ . . . . , . . . |
$$ . . . . . . . . |[/go]
So instead white can approach at 2-5 (or 2-4). Black can take the corner, but then white gets to extend down the side. Note that white wedging in at 4 instead of 3 is not so common these days. To atari from the inside as black, as in your first diagram, is slack, as was answering at 8, as white gets a 3 stone wall in sente to comfortably extend from. Instead atari from outside as in SoDesuNe's 2nd diagram is better. That sequence used to be considered joseki (it can also arise with different order from attach under 4-4 as first move) but now the pro opinion is the big corner is good for black. Another choice to take the corner is simply iron pillar at 4 instead of contact at 2. This way white doesn't get 3 in sente to help make a base on the side, but also black's corner is a little weaker/smaller.
The other choice for black is to take the outside with the shoulder hit, but usually white is happy to take the corner, particularly if black already had the keima shimari as it ends up too close to the wall (but is in a reasonable shape point for the turn at the top).
- Click Here To Show Diagram Code
[go]$$Wc Black wall
$$ -----------------+
$$ . . . . . . . . |
$$ . . . . . 7 . . |
$$ . . X . 6 5 . . |
$$ . . . . X . . . |
$$ . . . . . . 1 . |
$$ . . . . . 2 3 . |
$$ . . . . . 4 . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . , . . . |
$$ . . . . . . . . |[/go]
A quick comment on 2-4 vs 2-5. There are various subtleties, but the basic difference between these is that with the 2-5 white is guaranteed to get a position on the side, whereas with the 2-4 black has a choice of whether to let white go on the side or in the corner. So if the side is important you 2-5.
- Click Here To Show Diagram Code
[go]$$Wc 2-4, black choose corner (and reverts to one of 2-5 choices)
$$ -----------------+
$$ . . . . . . . . |
$$ . . . . . . a . |
$$ . . X . . . 4 . |
$$ . . . . X 2 1 . |
$$ . . . . . . 3 . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . , . . . |
$$ . . . . . . . . |[/go]
After the 2-4 black can bump and take the corner. Next white often clamps at a, I wrote about this at viewtopic.php?p=84568#p84568 . Black can also play a pincer as below, white could take the corner and in the diagram below can tenuki (as black only has a ko to kill) or live. Instead of living with 5 white can kosumi out between 2 and hoshi, but then black retakes the corner and attacks the running white group (but black's pincer stone is also weak).
- Click Here To Show Diagram Code
[go]$$Wc 2-4, black choose side
$$ -----------------+
$$ . . . . . . . . |
$$ . . . 8 7 . 5 . |
$$ . . X . 4 3 . . |
$$ . . . . X . 1 . |
$$ . . . . . . . . |
$$ . . . . . 6 2 . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . , . . . |
$$ . . . . . . . . |[/go]
There is not really a pincer against the 2-5 as white can 3-3 and is connected to the initial approach stone. Compare this to pincering the usual approach move. A common idea when pincered is to dodge to the corner, but then your initial approach stone gets cut off.
- Click Here To Show Diagram Code
[go]$$Wc pincer normal approach, cut
$$ -----------------+
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . 3 . . |
$$ . . . . X 4 . . |
$$ . . . . . . . . |
$$ . . . . . 1 . . |
$$ . . . . . . . . |
$$ . . . . . 2 . . |
$$ . . . . . . . . |
$$ . . . . , . . . |
$$ . . . . . . . . |[/go]
There was a game of mine where my opponent played this 2-5 approach and it was a really good move that took me by surprise: p18 on move 46 of http://www.online-go.com/games/board.php?boardID=320822. In that game I am trying to make territory on the top side, but white's move perfectly prevents that. If I play the shoulder hit I don't get much from the wall (due to white's strong group on the right side) and white easily lives in the corner and my top side is undermined. In the game I went for the corner, but in order to keep the top side my corner even ended up getting attacked!
In your game position, I'd need to see the whole board to make a judgement of if taking the outside could be ok for black, but locally speaking I feel black has to stop white from easily living in the corner, and therefore iron pillar at r16 is best (not s16 as that gives r15 sente which helps white live more, and the m17 stones means the corner weakness of iron pillar is not a problem).
- Click Here To Show Diagram Code
[go]$$Wc White Approaches at 2-4 with 1
$$ -----------------+
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ X . . . . . . . |
$$ X . . . X 2 . . |
$$ . . . . . . 1 . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . , . . . |
$$ . . . . . X . . |[/go]
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, securing a large corner and White has - in my opinion - no good move to make good shape locally.
, allowing White to Sabaki but taking a nice corner territory.
. After 'a' Black might push through at 'b' first and then capture. White will play 'c' for shape.
is generally also possible for Black.
at 
.