This does not sound like a reading problem, but more like an unclear understanding of how learning to read works, which is understandable considering that learning to read is a very complex process. I experienced the exact same thing at that point with my own son, now six, who just started reading shortly before his 6th birthday and after a long period of what you are describing.
As long as he is in school (kindergarten, preschool?), my advice is to be patient, supportive, keep reading to/with him, and stay in close touch with his teacher(s). They should be able to give you a very good breakdown of his progress, where he stands in respect to developmental milestones, and what you can/should do to support him (and what not to do).
Learning more about what is age and developmentally appropriate will help you better understand where your son stands.
An example of such information:
Kindergarten (Age 5)
Kids usually begin to:
- understand rhyming and play rhyming games
- match some spoken and written words
- understand that print is read from left to right, top to bottom
- write some letters and numbers
- recognize some familiar words
- predict what will happen next in a story
- retell stories that have been read to them
There is not enough information to make a conclusion, but from what you have provided, your son may be well on track to reading in a timely manner.