Ok so I'm not sure if I did this correctly, but this is my fsm for checking for "aAAAa". I didn't do the last half just in case this is incorrect. Forgive the mspaint w/mouse look. Red circle is initial start point. Purple is where it ends up if we succeed in getting "aAAAa" as the pattern.
Alright, good start.
Now consider how you might label each state with this problem. Right now you're using colors, but could you use numbers instead? Maybe label your start state as 0, and each subsequent state with an incremental number.
Next, try to run through your FSM with an example string. If we're only using As, take for example something like "aAaAAaAAAaAaA". As you do that, think about how you're keeping track of whether or not you're fulfilling your end condition or not.
I take pity on you so here's a slightly cleaner one for your use. Hopefully it's a little easier to keep track of: