Develop your head tone... and maybe take the song down about 2 whole steps.
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

"Anybody can play. The note is only 20 percent. The attitude of the motherfucker who plays it is 80 percent." -- Miles Davis

Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY
Remember: the diaphragm is just to help with the air. The air will vibrate your vocal cords, which can get thicker or thinner, producing lower or higher frequency soundwaves, respectively. Your diaphragm is very important, but it's only effective if you can get your vocal chords to the right thickness and allow them to vibrate freely. You may use your diaphragm perfectly and get your vocal chords thin enough to hit that C5, but if raise your larynx too much you may not sound good because your vocal chords will not have good space to vibrate, for example.

You said you're cracking. Cracking happens basically on two occasions: when you have bad air support, so your vocal chords will stop vibrating as there is not enough air going through or because your vocal chords can't go as thick or thin as you're trying to go, so they simply "fail" instead or giving you an "almost there" note. Imagine it like going to the gym: if you don't breathe properly you'll get tired quickly and if you try to lift more than you can your muscles just won't do it.
And the important thing here is that when you go to the gym you don't want to lift more than you can as it will lead to bad technique and, possibly, injuries. If you're cracking you have to take a step back and practice on lower or higher notes depending on where you're cracking and slowly build "strength" to get to where you want.

The only thing here you can do is practice, practice and practice, always aware of your present limits. I'd suggest working on your head voice, it's the simplest way I know to sing higher. You begin by singing with low volume, building mainly consistency. Don't worry about singing beautifully at the beginning, just focus on singing in tune in a relaxed manner. After you can sing the notes consistently without straining you begin to add power and shape to the tone.

In my opinion, from hearing the sample, head voice is exactly what's missing.
The thing about singing those high pitches is that it should take minimal effort. The trick is less air, not more. Pushing more air with your diaphragm will only result in a crap tone and probably give you nodules in the long run. Also remember the higher you go, the further back you should feel the note come out of your mouth if you get the configuration right. It shouldn't feel like it's going up, imagine it arcing instead. Once you get the hang of the configuration, you can put more air into it for a stronger sound.
Hi marshallmannen,

adding onto what everyone else has already provided you with, you should try doing exercises to train your head voice and connect them to your chest voice.
Here is what I do - sing to "ooh" and slide from one note to the same note one octave up and back. This is also called the siren and is effective in bridging between your two registers. Start of slowly at first because it will be weak but it will get stronger. If you would like more specific help you can check out two posts I've written here for a video guide!: http://superiorsingingsuccess.weebly.com/home/how-to-sing-better-for-guys and http://superiorsingingsuccess.weebly.com/home/how-to-sing-better-for-girls
Last edited by davidlwl94 at Jul 6, 2016,
While I'm no professional, but I have been studying vocals with a trainer ever since last year.

When hitting the high notes, breathe low into your back, its a mind over matter thing. Another thing is to make a smiling type of contour with your mouth to open up the hard pallatte. Though, you may find the vocalist in the song is singing the chorus in chest voice, in which case you'll have to lower the key or sing in head voice.

You're range in the verse was below my tessitura, and you went into head voice at the chorus (also my range), I'd probably place you as a baritone.