Python vs Java performace: brute force equation solver
An obvious possible improvement for both languages is storing the values to the fifth power (But I'm going to focus on python here). 

In python, while is a keyword and does not need parenthesis. Also, global lookup of methods is slower than local  lookup, so I would define pow = math.pow

pow = math.pow
while keep_searching:
    a += 1
    a5 = pow(a, 5)
    for b in range(1, a+1):
        b5 = pow(b, 5)
        for c in range(1, b+1):
            sum_begin = a5 + b5 + pow(c, 5)
            for d in range(1, c+1):
                sum = sum_begin + pow(d, 5)
                ...


Also note that python has an official style-guide, PEP8, which recommends putting spaces around operators and after commas in argument lists (I applied those rules in the code above).

Note that str.format does not care what it's parameters are. It will just call str on them and use that. So no need to call int on your parameters (they are already ints anyway).