5yr old probably has asthmatic cough are neti pots helpful-no other asthma symptoms so trying to find alternative help to avoid too much steroids etc?

Inhalers are OK. Several studies have shown minimal long term effects from properly used inhaled steroids in young children. They are much better than using oral prednisone. Again, control is best.
See your doctor. Cough can be many things beside asthma, including other lung disorders, heart disease, acid reflux, infection, foreign body, or many other issues, so you really need to see a doctor to see what is causing cough and what the options are.
Maybe. Netty pots are most helpful if there is a component of allergic rhinitis with a drippy nose. Then it is good to keep the nose clean, but unless the nasal allergis trigger a cough it probably won't help an asthmatic cough.
Not for asthma. If you're concerned that your child's cough may be due to asthma, please see your child's doctor. Rinsing out the nose with saline helps for coughs from post-nasal drip but won't help asthma. If a bacterial infection is causing the cough, antibiotics may be needed; asthma can be treated with a number of different meds, and inhaled steroids give a much lower dose than oral steroids.
May not need steriod. Steroids are generally used in asthmatics who have persistent symptoms that need a "controller" to reduce inflammation and the amount of "rescue inhaler" use. Regardless, if an inhaled steroid is needed, there appears to be excessive worry about side effects. The majority of the steroid (cortisone) stays in the lungs and does not get into the blood stream. Your pediatrician should be consulted.
Distilled water. There has been several answers/ opinions to your question. For the neti pot, donot use tap water please! several cases of deadly brain eating amebiasis have been documented.
No Neti Pots Not. No neti post will not help and you should follow up with Pediatrician or a Pediatric Pulmonologist or Allergist for the possible long term understanding and treatment of this condition in a 5 years old child and do what is best for the child.