having trouble with building a dropdown box that references days in a year and days in qtr

Hey guys,

I could very much use everyone's help. So I'm creating a dropdown box (Which I already know how to make, using data validation) for my spreadsheet that contain years from 2010 to 2020 in D5 (referenced from sheet2) and coressponding days in a year in E5 (referenced from sheet 2 using Vlook up). In F5, I have another dropdown box for each quarter: 1st, 2nd, 3rd and 4th (referenced from sheet 2) and days in quarter in cell G5: 90, 91, 92, 92 (using Vlook up from sheet 2).
Now hard part, the days in year E5 has to take into account the leap year (366 days in 2012, 2016 and 2020) which I managed to do also using the Vlookup. but for the the days in quarters (G5), I cant get the formula to factor in extra day in 1st quarter for the leap year. How can I resolve this? I uploaded whatever work i have done so far
Maybe using 2 IF formulas in G5 (days in qtr)?