Like it says on the tin. Problem? Basic configuration is not going to work. If I used several additional layers and all the Outer and Inner layers using carbon nanotubes, whereas the Middle Layer(s) use(es) Kevlar, Titanium or Aluminium, can they still survive incoming 5 kg guided projectiles of doom composed of depleted uranium?
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The Whipple shield is a form of spaced armour, causing the incoming projectile to give up part of its energy prior to impacting the main body of the ship. Because the physics of hypervelocity impacts is quite different from things travelling at velocities common to things moving on Earth, the normal form of a Whipple shield is a thin piece of aluminum held mechanically some distance from the ship's hull, rather than a heavy sheet of armour plate (like WWII German tanks often sported towards the end of the conflict).
Since the Whipple Shield is generally for dissipating the energy of micrometeors and small pieces of space debris, the thin shield of aluminum works well. The incoming particles are partially vaporized by the impact and what is left is broken up and dissipated in a cone, so the hull receives many small impacts rather than a large one.
The use of aluminum is more a matter of practicality rather than due to the material properties of the shield. Aluminum is relatively cheap, easy to form into the required shapes and most importantly, very light. With current and foreseeable technology, the most important consideration for spaceflight is the overall mass of the ship, so a Whipple shield shouldn't add too much extra mass to the vehicle.
The projectiles you are describing will have far more energy than a micrometeor or a small piece of debris. If you specify the velocity, the actual impact energy in Joules can be calculated, but it is safe to assume that even at "mere" orbital velocity the slug will have more energy than the binding energy holding the molecules of the shield together. The slug could be badly damaged or even vaporized by the impact, but the hypervelocity pellets of DU will still cause considerable damage to the ship. (Edit to add: At these velocities, it really doesn't matter too much what the slug is made of; 5Kg of kitty litter or wadded up paper towel will have just as much energy. The DU slug will have a smaller cross section, making it harder to get target lock, and the dissipated cone of debris will likely be tighter with DU).
There is a possible and practical method of using the idea of a Whipple shield to protect the ship, known as "Kirklin Mines". As described in Atomic Rockets:
In AV:T are kinetic weapons called "Kirklin mines" (invented by Kirk Spencer). They are dirt cheap chemical fueled anti-missile weapons, specifically anti-Torch missile weapons. The ideas is that they cost a fraction of the price of a missile, yet can scrag it. Using the magic of relative velocity, all they have to do is get in the way (this is why they are used against torch missiles, if the relative velocity isn't large enough the mine might not do enough damage to mission-kill the missile).
In your scenario, the Kirklin mines would be a simple chemical fuelled rockets or coilgun projectiles with an umbrella type structure on the front, launched in the path of the incoming projectiles. The impact should be far enough from the ship that the pieces of destroy slugs are dissipated in a large cone with very few striking the ship (ideally the ship has time to move out of the diameter of the cone and receives no strikes at all). Even if the relative velocity isn't large enough to destroy the incoming slug outright, the energy of the impact will probably cause it to break into several pieces, or cause it to tumble and change its orbit in an unpredictable manner and be more likely to miss the ship.
For more on space weaponry and space warfare, a good starting point is the Atomic Rockets site, specifically here: http://www.projectrho.com/public_html/rocket/spacegunconvent.php, but also look up Rocketpunk Manifesto's posts on space warfare: http://www.rocketpunk-manifesto.com/search?q=space+war