Your son is still too young to accurately test for dyslexia just because so many children that age have those problems and they naturally grow out of them. I am not discounting your worries. My sibs & have varying degrees of dyslexia in different forms so I'm aware of it. I have wondered if my oldest son could have it. He's almost 9 and has a host of other problems such as speech delay, developmental delays, fine motor delay, etc. He's old enough now that within the next year or so he doc can give me a referral to the local people I need to see. I am waiting longer just because of his delays because I want to make sure it's as accurate as possible.
HOWEVER, your son could have still have a problem even if it's not necessarily dyslexia. Haven't your sons school brought it up? Did they enroll him in a special education plan? Does he have or qualify for an IEP?
Have you had your son evaluated by a speech therapist, had his hearing and eyes checked, etc? I would start there if you haven't.
Also, be very careful of having a label applied to your child. Once that label is applied, it can not always be removed even it no longer really applies and the authorities really do treat your child differently. Some institutions will look at his record, see dyslexic (for instance) and then automatically only do things with him that they know work for dyslexics. They won't work with him in the way that is best for him and in the end will help build the rut that he could very easily get stuck in. I'm not saying everyone is like that but you have to be very prepared that it could easily be the case.
My sons first school was like that. They saw he had a speech delay and that he was ODD and that was that. THIS is how we deal with it and THIS is what we will do with him and THIS is what his schedule will be like regardless of how well it would work if we did it THAT way. However, his second school (he's been there 2 years now) is totally AWESOME! They have bent over backwards to provide him the services he needs in the ways that he responds to. They had his desk placed in a certain spot, he works with number lines on his story problems instead of drawing pictures or using manipulatives, and he's given multiple choice instead of fill in the blank, etc. His special ed teacher even ordered a completely new curriculum because he wasn't responding to the one she was using. And no, we don't attend a private or even especially affluent school.
Oh, and do keep in mind that a lot of research is starting to show that we push a little ones into school, especially the boys, too early and a lot of them aren't really ready to learn until they're around 7 even though they're considered at risk by then. For instance my youngest son was behind in his reading, they insisted he do Title I (because of state mandates) and then this year he had special ed. I wasn't really worried and he's actually made leaps and bounds this year. I see no problems with him catching up to his peers within the next school year. He'll turn 8 early this fall.
Like I said, talk to your sons doc, have him write some referrals to have eyes and hearing checked (not just by the doc, I mean professionally) and then go from there. The eyes could be easily impacting the reading if he needs glasses. As for the hearing, if that checks out just fine, then go with a speech therapist. They'll know what red flags to look for is he has an auditory processing disorder, etc. Also find a psychologist. They'll help a lot with helping your figure out what's going on with your son.