802.11a using the 5GHz band does NOT offer a higher data rate than 802.11n or 802.11ac which use the 2.4GHz or 5GHz band.
2.4GHz band offers more range and is better with walls etc.
There is no throughput benefit to either band other than as described.
In terms of data throughput 802.11a is I think identical to 802.11g (also 2.4GHz) and offers up to 54Mbps (bits per second) instantaneous data rate and about half that as a practical maximum achievable throughput. It may well be exactly half but I am not sure.
The point of 802.11a was to permit more channels and to avoid the interference of the already widely used 2.4GHz band. 802.11a is often used by businesses using professional grade kit and professional installations. Consider it if you get too much interference on the 2.4GHz bands.
Now to your little problem.
If you are getting 35Mbps you are definitely on something better than a/b/g. The best that any of them can do is about half of 54Mbps and 35 is well over that so you must be on 802.11n since your machine does not support 802.11ac (According to Mr Saab D).
1. Check that your radio is not set on some power saving mode.
This is described nicely here:-
WiFi Remedies for Samsung Laptops | NotebookReview
Note the two sections on power saving.
You could consider a driver upgrade also described there but you may need to get in some expertise.
2. Test at a shorter range (say 5 feet) and report results.