Antenna Matching: This is a gamma match antenna you can use the same gamma match I used for building the 4 Elements Gamma Match Yagi you may open the link here: https://dw1zws.com/building-the-gamma-match-for-4-elements-yagi/
To obtain the antenna pattern and approximate gain I used 4NEC2
For the SWR results and measurement of this 5 Element 2m VHF Yagi you may see it here on the link below:
https://dw1zws.com/5-elements-yagi-swr-response/