There is a lot of good advice here. I didn't read anything that would be really bad advice. However, there are a couple of key considerations in your case. This is your first serious system, and you are working with a fairly low budget. Therefore, I suggest that you look to the future. In other words, this won't be your final, maybe not even a long term, system. I would try to get one or two components out of this that will serve you well for years to come. The other thing I have noted is that you are going to be using a small bedroom. In view of that later consideration, I would avoid speakers that go much below about 40Hz. Speakers that go low can be very difficult to integrate into a small room. You can have really good speakers sound really bad in a room like yours because of too much ringing in the low frequencies. You may also want to eliminate speakers that need a lot of space between them and room boundaries. Given this, I would probably forget about panel (dipole) speakers. There are some good relatively inexpensive monitors that might work very nicely in your room. It is important to hear speakers before buying. If there are some good salons within driving distance, spend some time finding a speaker that you like that will work well in your room. Try to negotiate an in home audition. Your speaker decision will dictate where you need to be looking with respect to an integrated amp. Some speakers like tubes, some almost demand solid state. The Coincident Dynamo mentioned by Charles is a superb value and can take you years down the road. But, you really are going to need a high efficiency (~92 to 94 dB) high impedance (8 Ohm) speaker. I use a dynamo in my second system. It is a really nice little amp. Both the Marantz 8005 and Sony HAPZ1 have been mentioned earlier. I haven't heard the Marantz, but I can tell you the Sony is superb. I had my Sony modded by Dan Wright, but it was a superb value at 2K before modification. Both the Sony and Marantz offer a serious upgrade path by sending them to ModWright down the road. There is no doubt, you can get a very nice little system for 5K. Just be mindful of the limitations imposed by your room, and you should be fine.
