My son just started hockey and my pictures are very dark and grainy. The lights are dim. Was looking to get another camera and lens to take better pictures. Would like to stay under $5,000. Any suggestions?
If you are shooting ice hockey the exposure is probably biased by the white ice. Before you spend any money try to use the camera's exposure compensation to make the pictures lighter.
The Wikipedia article starts with an example which is pretty close to your problem (shooting snowy mountains).
Here are some more explanations on exposure compensation.
The best way to shoot indoors sports in most fairly evenly lit gyms/rinks/arenas is to set exposure manually. It gives you the most complete control over shutter times, aperture, and ISO.
Keep in mind that manual exposure will be more accurate than automatic metering under flickering lights such as those found in most indoor sports arenas and outdoor stadiums used at night. The meter will often measure the lights at their peak and then the shutter will open when they are in the valley of their cycle and vice-versa. Setting manual exposure for the middle of the lights' cycle will get you closer overall for all of your shots.
There are cameras that measure the flicker of the lighting and time the shutter to open when the lights are at their peak. Most of them are Canon models. The 7D Mark II introduced the feature in late 2014 and most upper tier bodies (1DX Mark II, 5D Mark IV, 6D Mark II, 90D, 80D, 77D) and even a few "Rebels" (T6i/750D, T6s/760D, T7i/800D) include it. Nikon's D500 and D5 have a similar feature as does the Sony α9. Note that there are other cameras that have a "flicker reduction" feature that is only applicable to video shooting, but does not works when shooting stills.
If you want to get anywhere close to freezing the action you're just going to have to live with whatever flicker the lights are giving you. To eliminate most of the flicker you would need to use shutter times of about 1/125 second or longer/"slower" and that's not happening with ice hockey. If you can get the shots you want shooting raw that will give you more latitude to correct the color and exposure of the peaks and valleys of the lights in post-processing. (The linked question is about how to process hockey photos shot under marginal lighting. The answer shows an example of the power of raw post processing vs. jpeg.)
Of course shooting raw will lower the number of frames you can take in a burst before your buffer fills up and your frame rate bogs down. Normally you'll want to avoid filling the buffer completely, though. Try to limit your bursts to about half that so you will have a few shots in reserve if a key action moment happens.
You can set a custom white balance by shooting directly at a solid white, glare free section of ice. Intentionally underexpose a stop or two, set the focus switch on the lens to "MF" and defocus at either the MFD or infinity. If the lights in the venue flicker (they probably will - our eyes can't tell the difference but our cameras sure can!) take several shots and use a shot that is about halfway in between the brightest and darkest one to set the custom WB.
Don't forget to switch the lens back to "AF" when you've got the WB set. While you're at it, set the Image Stabilization to "On", the IS mode to panning mode if your camera/lens combo offers it, and the focus limiter, if available, to limit very close focus distances (unless your subjects will be closer to you than the focus limiter threshold at points in the action).
Unless you have a super telephoto lens (over 300mm) you're not going to get many tight shots unless the players are on the closest parts of the ice to where you are. If you plan on cropping shots of players further away your maximum shutter times will need to get shorter to control blur from subject motion than they would be for uncropped shots.
You're probably going to want to manually select the center AF point only and leave it there. Set the AF mode to AI Servo AF or AF-C (or whatever your camera maker calls "continuous AF"). You'll need to keep your main subject in the center of the frame. For distant shots you're probably going to crop a bit anyway, so you can adjust the composition if you want by cropping off-center. If you set the AF point selection to Auto you'll wind up with the closest thing in the frame (usually a plexiglass support) instead of your intended subject in focus. When shooting action I prefer to use the AF ON button to initiate AF and disable AF connected to the shutter button but it takes a bit of getting used to it. YMMV.
Set the drive mode to Continuous/Burst.
Set your aperture to f/2.8, set your shutter time to 1/1000 and then dial up the ISO until you get a decent histogram on the back of the camera when reviewing your shots. Avoid the +1/3 stop ISO settings on Canon DSLRs. Keep in mind that if you are shooting at a downward angle with most of the frame consisting of white ice you'll need the histogram to be shifted a bit to the right. If you're shooting from a very low angle such as the team bench and a lot of the frame is a dark background (such as dimly lit seating areas) you'll want a histogram more to the left. If 1/1000 second forces you into an ISO higher than you're willing to accept, reduce the shutter time to 1/800, 1/640, or 1/500 second and check your results. When reviewing your shots on the LCD, zoom in all the way to see how much motion blur you're getting.
Don't be afraid to take plenty of frames. Under the best of circumstances the "keeper" rate is lower for sports than most other kinds of photography. But that doesn't mean you shouldn't plan your shots instead of just "praying and spraying." It just means you should accept that sometimes the action will move a different way than you anticipated. Sometimes the AF will miss a little. Sometimes it will miss by a country mile. Sometimes another player (or, even more likely, a referee with his back to you) will pass between you and your subject at the exact instant the shutter is open.