I've been facing these problems in a big way myself, ever since my group fully embraced 5th edition, our IG player got back to playing games, and our Tyranid player actually read the Tervigon entry fully. Necrons did take a big hit, in my opinion, but Moc and Gutstikk helped me out a bit, and I think that going in with a 5th edition mindset to begin with really helps.
First of all, volley fire can't be relied on like in past editions. Tau and Necrons both rely on it pretty heavily, but universal cover saves usually cut its efficiency in half (fortunately for Tau, they can markerlight cover away, but Necrons have no such luck). This means that Destroyers, one of our old stand-byes, will only be half as effective at swarm killing, one of their primary functions. Because the three swarmiest armies in the game are now all very competitive, this puts us in a hard situation. Wraithwing, a tactic where the Necron player fills out his Fast Attack slots with Wraiths instead of Destroyers (and a tactic which I never really liked before) has become perhaps more viable than the traditional Destroyer-heavy army. Furthermore, I find opponents so fast now that Immortals and Warriors have lost a lot of their potency as well.
As for the Monoliths, I find that to be something of a toss-up. They're even harder to kill than they used to be, which is really nice for contesting objectives or driving inexorably up the middle. However, what made the Monolith really special (in my view) was the complete control over melee that it used to give the Necron player. Because Necron units (primarily Warriors) are no longer reliable to take a few turns of abuse in close combat, you can't use them as a buffer for melee armies anymore, which used to be one my main tactics (move forward to meet the enemy assault, move all of your fire power to safety, then teleport the Warriors out of harm's way and open up).
One way to overcome the fact that our shooting isn't as effective and that we aren't as strong in CC is simply changing the way you look at Necron strategy, something which took me a long time to get used to. Melee is no longer a controllable current that you can stymie using unkillable Warrior units and teleportation tricks, but now something you'll need to meet head-on and may need to bank on winning a few. Wraiths can be good for this, not to mention Tomb Spyders and C'tan (some will argue for Pariahs, which I've always found to be a cool unit, but mine always die before they make it within ability-range).
So, rather than being a volley army as we were in past editions, it might be worthwhile for your friend to look into alternative playstyles. If you plan to rely on Wraiths, taking other army elements which make soften up their enemies may be crucial. I went from Warrior/Destroyer/Monolith centric armies to a Wraith/Heavy Destroyer/Combat Lord setup, having just accepted that every opponent I had was going to shrug off my Destroyer and Immortal fire like it was nothing, meaning I needed to get up to where there were no cover saves. I basically just ignore swarms at range anymore, since I can't find a cost-effective way to kill them. Tomb Spyders are good against Marines, I've heard (we don't have many in my group), and Monoliths can still be pretty intimidating. If he looks into alternative unit selections and army viewpoints, I think he can still do well even against 5th edition armies, though I do suspect he will continue to be the underdog since the Necron codex is comparatively dated.
Bear objectives in mind, too. I often spend the entire game losing only to pull a draw or a win at the last second because I used my Flayed Ones to Outflank and grabbed or contested a Control Point, used Veil of Darkness to do the same, used my Monolith as an unkillable hunk of living metal to camp out on an objective, or made sure to get my damaged units out of the danger zone before my enemy could claim their killpoint.