Here is a Python program that converts a byte array to its equivalent hexadecimal representation: 

def byte_array_to_hex(byte_array):
    hex_str = ""
    for byte in byte_array:
        hex_str += "{:02x}".format(byte)
    return hex_str

byte_array = bytearray([10, 20, 30, 40, 50])
hex_representation = byte_array_to_hex(byte_array)
print(hex_representation)

This program defines a function byte_array_to_hex that takes a bytearray as input and returns its hexadecimal representation as a string. The function loops through each byte in the input bytearray, and converts each byte to its hexadecimal representation using the format method with the "{:02x}" format string. The 02 specifies that the output should be zero-padded to two characters, and the x specifies that the output should be in hexadecimal. The hexadecimal representation of each byte is then concatenated to form the final hexadecimal string.