It is a shame that your current pediatrician did not refer you to the state early childhood intervention agency before he turned 3. The state provides early testing, evaluation and intervention services from newborn to age 3. However, after age 3 it is provided through your local school district. My 7 year old daughter has similar issues and received therapies as an infant and then at age 3 was enrolled in a special preschool program through the school district that got her ready for regular school. If I were you, while searching for the perfect pediatrician, contact your local Mesquite school district NOW, before school is out for summer, and tell them you want your child evaluated. If they hesitate, you must insist, because you are well within your rights to receive it. Chances are, if he turns 5 in August, he may not be ready to start Kindergarten in the fall if he is delayed like you say. The school district provides a special preschool program called PPCD (preschool program for children with disabilities) through age 5. My daughter benefitted tremendously from that program, once we found the right one. The first PPCD they put her in was terrible. The second one was wonderful.
It may be that there is nothing wrong with him that a little time won't mature...and wouldn't that be great? However, if there is something else going on, like with my daughter, it's best to nip it in the bud as early as possible. Good luck and keep me informed.
Remember that you are your child's best advocate. You have to listen to your heart. You are the only one who loves him as much as you do. If I only listened to my daughter's pediatrican we wouldn't have found out about her cranial synastosis which required surgery.
God Bless.