H1B Cap exempt visa application for future dates - 6 year limit

Hi Team,

I have travelled to India in Nov 2020 from US. I was on H1b visa and have consumed 5 years 7 months of my 6 years of H1B visa. i still have 5 months left on my H1B visa.
I am continuing my work with the same client and same organization from India.
I received my petition in 2013 but travelled to US in 2014
i want to travel to US from May 2021 and use these 5 months of recapture period to work in the same project from May 2021 to Sep 2021.
Can you please let me know if I can apply in Dec for H1b cap exempt in this scenario for future dates of May-Sep 2021

Yes, you can as long as you have not used up all your 6 year time limit.
You need to work with your attorney to make sure they submit all your dates and previous stay in US, so that they do not miss out any months.