05 CR-V uses the K24 engine, which is also found in Accords and some other Honda/Acura vehicles. It's one of the most bulletproof 4-cylinder engines out there, and it uses a timing chain which does not need to be changed like a timing belt. That same engine debuted in 2002 and a very similar variant is still being used in Accords and CR-Vs today!
As for oil, any name brand conventional or synthetic blend will work fine. No need to use full synthetic. For oil changes, 5,000-7,500 miles is a good range to go by. If you want to use an oil that's widely available and similar to the "Honda-brand" oil dealerships use, look for Ford Motorcraft Synthetic Blend 5W-20 at Walmart and other places. It's made by ConocoPhilips, just like the OEM oil, and it's cheap at about $16 for 5 quarts.
Maintenance items to do if they have not been done:
-Change air filter if it is dirty. Same with cabin air filter (if the SE has one).
-Change rear differential fluid if your CRV is AWD. I did this on a 09 CRV and it used Honda Dual Pump II fluid. The 2005 should use the same stuff. This is very important to do every 20-30k miles. Honda really over-stretched the diff fluid change interval on early CR-Vs and reduced the interval on later years to a more reasonable one.
-Change the automatic transmission fluid. Make sure to use Honda DW-1. Do not use any kind of power-flushing procedure; only drain and refill is recommend by Honda. A single drain and refill will replace about 50% of the old fluid due to fluid being stuck in the torque converter. 3x drain and refill will swap out about 90% of the old fluid. I recommend doing a single drain and refill every 30-40k miles.
-(Optional) Change the ATF filter. Most dealerships don't even know that there is a filter for the ATF, but it's pretty easy to change on Accords and CR-Vs. I did it on my Accord and it was a 20-minute preocedure. My philosophy is that if you are going to change the ATF, you might as well change the ATF filter along with it since the part is under 20 bucks and relatively easy to change. The part # should be 25430-PLR-003, but double check this yourself to make sure.
-Change coolant and spark plugs if the car has more than 100k miles and has not had those done.
-Change brake fluid if it has not been done in the past 3 years. Honda recommends to do this every 3 years because brake fluid is hygroscopic and absorbs water over time.