Sure, I can help you with that.
**a) Determine ultimate moment**
The ultimate moment is given by:
```
Mu = 1.5 * 10 * 5 + 1.2 * 5 = 85 kNm
```
**b) Determine moment reinforcement (if singly reinforced provide T12 hangers)**
The moment reinforcement can be determined using the following formula:
```
As = Mu / fy * d = 85 / 500 * 480 = 6.88 cm^2
```
The nearest standard size of reinforcement is T12, which has an area of 7.6 cm^2. Therefore, the beam will be singly reinforced with T12 hangers.
**c) Design shear reinforcement**
The shear reinforcement can be designed using the following formula:
```
Vs = 0.15 * 12 * 5 = 9 kN
```
The minimum shear reinforcement is given by:
```
Asv = 0.2 * 250 * 480 / 1000 = 24 cm^2
```
The nearest standard size of shear reinforcement is No. 8 stirrups, which have an area of 0.15 cm^2. Therefore, the beam will be provided with 16 No. 8 stirrups spaced at 200 mm c/c.
**d) Check deflection**
The deflection can be checked using the following formula:
```
L/d = 5000 * Mu / fy * Ec * b * d^2
```
Substituting the values, we get:
```
L/d = 5000 * 85 / 500 * 250 * 480^2 = 0.041
```
The allowable deflection is 0.045, so the beam is satisfactory in terms of deflection.
Therefore, the design of the beam is complete.