There are two steps:
1. Create md5 data from a string
2. Covert the md5 data to a hex string

Swift 2.0:

func md5(string string: String) -> String {
    var digest = [UInt8](count: Int(CC_MD5_DIGEST_LENGTH), repeatedValue: 0)
    if let data = string.dataUsingEncoding(NSUTF8StringEncoding) {
        CC_MD5(data.bytes, CC_LONG(data.length), &digest)
    }

    var digestHex = ""
    for index in 0..<Int(CC_MD5_DIGEST_LENGTH) {
        digestHex += String(format: "%02x", digest[index])
    }

    return digestHex
}

//Test:
let digest = md5(string:"Hello")
print("digest: \(digest)")

Output:

digest: 8b1a9953c4611296a827abf8c47804d7

Swift 3.0:

func MD5(string: String) -> Data {
    let messageData = string.data(using:.utf8)!
    var digestData = Data(count: Int(CC_MD5_DIGEST_LENGTH))

    _ = digestData.withUnsafeMutableBytes {digestBytes in
        messageData.withUnsafeBytes {messageBytes in
            CC_MD5(messageBytes, CC_LONG(messageData.count), digestBytes)
        }
    }

    return digestData
}

//Test:
let md5Data = MD5(string:"Hello")

let md5Hex =  md5Data.map { String(format: "%02hhx", $0) }.joined()
print("md5Hex: \(md5Hex)")

let md5Base64 = md5Data.base64EncodedString()
print("md5Base64: \(md5Base64)")

Output:

md5Hex: 8b1a9953c4611296a827abf8c47804d7
md5Base64: ixqZU8RhEpaoJ6v4xHgE1w==

Swift 5.0:

import Foundation
import var CommonCrypto.CC_MD5_DIGEST_LENGTH
import func CommonCrypto.CC_MD5
import typealias CommonCrypto.CC_LONG

func MD5(string: String) -> Data {
        let length = Int(CC_MD5_DIGEST_LENGTH)
        let messageData = string.data(using:.utf8)!
        var digestData = Data(count: length)

        _ = digestData.withUnsafeMutableBytes { digestBytes -> UInt8 in
            messageData.withUnsafeBytes { messageBytes -> UInt8 in
                if let messageBytesBaseAddress = messageBytes.baseAddress, let digestBytesBlindMemory = digestBytes.bindMemory(to: UInt8.self).baseAddress {
                    let messageLength = CC_LONG(messageData.count)
                    CC_MD5(messageBytesBaseAddress, messageLength, digestBytesBlindMemory)
                }
                return 0
            }
        }
        return digestData
    }

//Test:
let md5Data = MD5(string:"Hello")

let md5Hex =  md5Data.map { String(format: "%02hhx", $0) }.joined()
print("md5Hex: \(md5Hex)")

let md5Base64 = md5Data.base64EncodedString()
print("md5Base64: \(md5Base64)")

Output:

md5Hex: 8b1a9953c4611296a827abf8c47804d7
md5Base64: ixqZU8RhEpaoJ6v4xHgE1w==

Notes:
#import <CommonCrypto/CommonCrypto.h> must be added to a Bridging-Header file

For how to create a Bridging-Header see this SO answer.

In general MD5 should not be used for new work, SHA256 is a current best practice.

Example from deprecated documentation section:

MD2, MD4, MD5, SHA1, SHA224, SHA256, SHA384, SHA512 (Swift 3+)

These functions will hash either String or Data input with one of eight cryptographic hash algorithms.

The name parameter specifies the hash function name as a String
Supported functions are MD2, MD4, MD5, SHA1, SHA224, SHA256, SHA384 and SHA512
a
This example requires Common Crypto
It is necessary to have a bridging header to the project:
#import <CommonCrypto/CommonCrypto.h>
Add the Security.framework to the project.

---

---

This function takes a hash name and String to be hashed and returns a Data:

name: A name of a hash function as a String  
string: The String to be hashed  
returns: the hashed result as Data  

func hash(name:String, string:String) -> Data? {
    let data = string.data(using:.utf8)!
    return hash(name:name, data:data)
}

Examples:

let clearString = "clearData0123456"
let clearData   = clearString.data(using:.utf8)!
print("clearString: \(clearString)")
print("clearData: \(clearData as NSData)")

let hashSHA256 = hash(name:"SHA256", string:clearString)
print("hashSHA256: \(hashSHA256! as NSData)")

let hashMD5 = hash(name:"MD5", data:clearData)
print("hashMD5: \(hashMD5! as NSData)")

Output:

clearString: clearData0123456
clearData: <636c6561 72446174 61303132 33343536>

hashSHA256: <aabc766b 6b357564 e41f4f91 2d494bcc bfa16924 b574abbd ba9e3e9d a0c8920a>
hashMD5: <4df665f7 b94aea69 695b0e7b baf9e9d6>