We've been told that an organisation should not go directly for CMMI level 5. Could you please confirm this and also tell us if any statement is available to substantiate the above?
Also, please clarify why we need to certify at Level 3 first and then target to Level 5.
Wow, we've got some over-achievers out there!
Like many things in the CMMI model, the advice you heard includes the words "should not" and not the words "can not." There is no policy from the SEI that explicitly says "you cannot go directly to ML 5," so, by definition, it is possible to do so.
Should you do it? That's a completely different discussion. I believe it's a mistake to do so because organizations can't change overnight, it takes time to absorb change, and you will often get a much better return on investment if you take a measured, gradual, and iterative approach to process improvement.
HOWEVER (and this is important) the SEI has declared that companies who pop-up as ML 5 for the first time that have never had a formal appraisal in the past will be subject to additional auditing and scrutiny. If they find that your appraiser should not have awarded you ML 5 then they will revoke it. This is not a problem if you really are performing at Level 5 . . . but there are numerous examples of this happening and the appraisal was, in fact, not valid.
Beware of the Lead Appraiser who recommends this type of approach. In my opionion someone that advises you to jump right to ML 5 is either un-ethical or, even worse, ignorant (this is by far the bigger problem). Achieving ML is (and should be) extremely difficult and while its effects can be very positive, it is a lengthy journey.
The answer to your ML3 question is the same. Not required, but highly recommended. ML3 provides you with a foundation for consistent process performance, something required to achieve ML 4 and ML5.
If I were working with your company I would want to know why this is important to you. If it's to save on appraisal costs, then this is not the solution. Appraisal costs are roughly 10% of your overall process improvement effort - hardly worth even worrying about.
Best of luck.