Passing a lambda into a function template

I'm learning C++, and I'm trying to implement a binary search function that finds the first element for which a predicate holds. The function's first argument is a vector and the second argument is a function that evaluates the predicate for a given element. The binary search function looks like this:

template <typename T> int binsearch(const std::vector<T> &ts, bool (*predicate)(T)) {
    ...
}

This works as expected if used like this:

bool gte(int x) {
    return x >= 5;
}

int main(int argc, char** argv) {
    std::vector<int> a = {1, 2, 3};
    binsearch(a, gte);
    return 0;
}

But if I use a lambda function as a predicate, I get a compiler error:

search-for-a-range.cpp:20:5: error: no matching function for call to 'binsearch'
    binsearch(a, [](int e) -> bool { return e >= 5; });
    ^~~~~~~~~
search-for-a-range.cpp:6:27: note: candidate template ignored: could not match 'bool (*)(T)' against '(lambda at
      search-for-a-range.cpp:20:18)'
template <typename T> int binsearch(const std::vector<T> &ts,
                          ^
1 error generated.

The above error is generated by

binsearch(a, [](int e) -> bool { return e >= 5; });

What's wrong? Why is the compiler not convinced that my lambda has the right type?