Using MINIFS function
=MINIFS(A3:E3,A2:E2,1,A1:E1,"A")
Alternative
1] MIN+IF function array formula (Ctrl+Shift+Enter)
{=MIN(IF((A1:E1="A")*(A2:E2=1),A3:E3))}
2] AGGREGATE function normal formula
=AGGREGATE(15,6,A3:E3/(A1:E1="A")/(A2:E2=1),1)
Regards